🔑:## Step 1: Determine the initial weight on the balanceThe initial weight on the balance is the weight of the cup of water, which is given as X.## Step 2: Calculate the weight of the stone and the displaced waterWhen the stone is immersed in the water, it displaces water of weight Z. The weight of the stone in the air is given as Y.## Step 3: Apply Archimedes' PrincipleAccording to Archimedes' Principle, the buoyant force (or upthrust) on the stone is equal to the weight of the fluid (water in this case) displaced by the stone. This means the stone will experience an upward force equal to the weight of the water it displaces, which is Z.## Step 4: Determine the new weight on the balanceWhen the stone is fully immersed and sinks to the bottom of the cup, its weight (Y) is added to the system (cup + water), but because it displaces water of weight Z, the effective weight added to the initial system (cup of water) is Y - Z (since the buoyant force reduces the apparent weight of the stone by the weight of the displaced water).## Step 5: Calculate the new reading on the balanceThe new reading on the balance will be the initial weight of the cup of water (X) plus the effective weight added by the stone (Y - Z).The final answer is: boxed{X + Y - Z}

🔑:## Step 1: Understand the problem and the given informationWe are tasked with finding the minimum photon energy required to dissociate deuterium into a proton and a neutron. The binding energy of deuterium is given as 2.22 MeV, and the rest energies for the proton and neutron are 938 MeV and 939 MeV, respectively. We need to consider two cases: (1) both the proton and neutron acquire collinear equal velocities parallel to the photon momentum, and (2) the neutron remains stationary after the collision.## Step 2: Calculate the minimum photon energy for case 1In the first case, where both the proton and neutron acquire collinear equal velocities, we need to consider the conservation of energy and momentum. The photon energy (E) must be greater than or equal to the binding energy of deuterium (2.22 MeV) plus the energy required to give the proton and neutron equal velocities. However, since the photon must provide at least the binding energy to break the deuterium, and any additional energy will go into kinetic energy of the products, the minimum photon energy will be slightly more than the binding energy due to the requirement for momentum conservation and the mass-energy equivalence.## Step 3: Apply the conservation of energy and momentum for case 1For case 1, the momentum of the photon must equal the combined momentum of the proton and neutron after the collision. Given that the photon's momentum (p) is related to its energy (E) by p = E/c, and the momentum of a particle is given by p = γmu, where γ is the Lorentz factor, m is the rest mass, and u is the velocity, we can set up equations based on these principles. However, the key insight is recognizing that the minimum energy photon that can dissociate deuterium must have an energy equal to the binding energy plus the minimum kinetic energy required for the proton and neutron to move, taking into account relativistic effects.## Step 4: Calculate the minimum photon energy for case 2In the second case, where the neutron remains stationary, the photon's energy must be sufficient to break the deuterium bond and impart enough energy to the proton to carry away the momentum of the photon. The energy required is at least the binding energy of deuterium (2.22 MeV) plus the kinetic energy needed for the proton to have the same momentum as the photon before the collision.## Step 5: Apply the conservation of energy and momentum for case 2For case 2, since the neutron is stationary after the collision, all the momentum of the photon is transferred to the proton. The minimum photon energy can be calculated by considering the threshold energy required for the reaction, which is the binding energy of deuterium plus the energy needed to give the proton the necessary momentum.## Step 6: Determine the minimum photon energy requiredGiven that the binding energy of deuterium is 2.22 MeV, and considering the rest masses of the proton and neutron, the minimum photon energy required to dissociate deuterium into a proton and a neutron, taking into account the need to conserve both energy and momentum, will be slightly above this binding energy due to the kinetic energy requirements for the products. However, the exact minimum energy will depend on the specifics of the collision, including the velocities of the products.## Step 7: Consider relativistic effects and threshold energiesIn both cases, relativistic effects become significant at high energies. The threshold energy for the reaction, where the products have minimal kinetic energy, is essentially the binding energy of deuterium. Any energy above this threshold will go into kinetic energy of the proton and neutron.## Step 8: Calculate the threshold energyThe threshold energy for photodissociation of deuterium, considering the neutron remains stationary, can be found by equating the photon energy to the energy required to break the deuterium bond and impart momentum to the proton. This energy is essentially the binding energy of deuterium, as the minimum energy required to break the bond without considering the kinetic energy of the products.The final answer is: boxed{2.22}

🔑:To understand how the interference pattern changes when the distance between the slits in a double-slit apparatus is increased from d to 2d, we must delve into the principles of quantum mechanics, particularly the concept of wave-particle duality and the de Broglie hypothesis. The de Broglie hypothesis states that particles, such as electrons, can exhibit wave-like behavior, with a wavelength λ given by λ = h / p, where h is Planck's constant and p is the momentum of the particle.The interference pattern observed on the screen behind the slits is a result of the electron's wave-like behavior. When an electron passes through the double slits, it creates two coherent wave sources. These waves then interfere with each other, resulting in an interference pattern on the screen. The pattern consists of bright and dark fringes, corresponding to regions of constructive and destructive interference, respectively.The condition for constructive interference (bright fringes) is given by the equation:[ d sin(theta) = n lambda ]where (d) is the distance between the slits, (theta) is the angle from the central maximum to the point of interest on the screen, (n) is an integer (n = 0, ±1, ±2, ...), and (lambda) is the de Broglie wavelength of the electron.When the distance between the slits is increased to 2d, the equation for constructive interference becomes:[ 2d sin(theta) = n lambda ]To maintain the same energy (and thus the same de Broglie wavelength (lambda)), the momentum of the electron must remain constant, as the energy of a particle is related to its momentum by (E = p^2 / (2m)) for non-relativistic particles, where (m) is the mass of the electron.Given that (lambda = h / p), if the energy (and thus (p)) of the electron remains constant, (lambda) also remains constant. Therefore, the change in the interference pattern is solely due to the change in (d), the distance between the slits.Increasing (d) to (2d) means that for the same angle (theta), the path difference between the waves from the two slits is doubled. To achieve the same condition for constructive interference (i.e., (n lambda)), the angle (theta) must decrease because (2d sin(theta) = n lambda). This implies that the interference fringes will move closer to the central maximum.In more detail, the spacing between the fringes (the distance between two consecutive bright or dark fringes) is inversely proportional to the distance between the slits. The fringe spacing (Delta y) at a distance (L) from the slits can be approximated by:[ Delta y = frac{lambda L}{d} ]When (d) is doubled, (Delta y) becomes:[ Delta y' = frac{lambda L}{2d} = frac{1}{2} Delta y ]This means that the fringe spacing is halved when the distance between the slits is doubled, assuming the screen's distance (L) from the slits and the electron's energy (and thus (lambda)) remain constant. As a result, the interference pattern becomes denser, with more fringes appearing within the same interval on the screen.In summary, increasing the distance between the slits from (d) to (2d) while keeping the electron's energy (and thus its de Broglie wavelength (lambda)) constant leads to a denser interference pattern. The fringes move closer together, with the spacing between them halving due to the increased path difference for the same angle of deviation from the central maximum. This phenomenon is a direct consequence of the wave-like behavior of electrons as described by quantum mechanics and demonstrates the principles of interference and diffraction that govern the behavior of wave functions in such experiments.

🔑:The impact of Foreign Direct Investment (FDI) on China's economic growth from 1982 to 2017 has been significant, with FDI playing a crucial role in the country's rapid economic development. This analysis will examine the effects of FDI on China's GDP, fixed investment, and regional development, as well as the positive and negative consequences of FDI in the marketplace.Effects on GDP:FDI has contributed substantially to China's GDP growth, with the country becoming one of the largest recipients of FDI in the world. According to the National Bureau of Statistics of China, FDI inflows increased from 636 million in 1982 to 136.3 billion in 2017, with an average annual growth rate of 17.3%. This influx of foreign capital has helped to stimulate economic growth, with FDI accounting for approximately 10% of China's GDP growth between 1982 and 2017.Effects on Fixed Investment:FDI has also had a significant impact on China's fixed investment, with foreign investors contributing to the development of the country's infrastructure, manufacturing sector, and service industry. FDI has helped to increase China's fixed investment, with the country's fixed investment growth rate averaging 15.6% per annum between 1982 and 2017. This has enabled China to upgrade its industrial structure, improve its competitiveness, and enhance its economic efficiency.Effects on Regional Development:FDI has played a crucial role in promoting regional development in China, with foreign investors helping to bridge the economic gap between the coastal and inland regions. The coastal regions, such as Shanghai, Guangdong, and Jiangsu, have been the primary recipients of FDI, with these regions accounting for approximately 70% of China's total FDI inflows between 1982 and 2017. However, in recent years, the Chinese government has implemented policies to encourage FDI in the inland regions, such as the "Go West" strategy, which has helped to promote economic development in these areas.Positive Consequences of FDI:1. Job Creation: FDI has created millions of jobs in China, both directly and indirectly, contributing to a significant reduction in unemployment rates.2. Technology Transfer: FDI has facilitated the transfer of advanced technologies, management expertise, and innovative practices, enabling Chinese firms to improve their competitiveness and productivity.3. Market Access: FDI has provided Chinese firms with access to international markets, enabling them to expand their export base and increase their global market share.4. Infrastructure Development: FDI has contributed to the development of China's infrastructure, including transportation networks, telecommunications, and energy systems.5. Economic Diversification: FDI has helped to diversify China's economy, reducing its dependence on traditional industries such as textiles and manufacturing.Negative Consequences of FDI:1. Environmental Degradation: The influx of FDI has led to environmental degradation, with foreign investors often prioritizing economic growth over environmental protection.2. Income Inequality: FDI has exacerbated income inequality in China, with the benefits of economic growth often accruing to a small elite, while the majority of the population remains disadvantaged.3. Dependence on Foreign Capital: China's reliance on FDI has created a dependence on foreign capital, making the country vulnerable to fluctuations in global economic trends.4. Loss of Domestic Industries: The influx of FDI has led to the decline of domestic industries, as foreign firms have acquired or displaced Chinese companies, leading to a loss of domestic employment and economic opportunities.5. Cultural Homogenization: FDI has contributed to cultural homogenization, with foreign firms often imposing their cultural values and practices on Chinese society, leading to a loss of cultural diversity and identity.Conclusion:In conclusion, FDI has had a significant impact on China's economic growth from 1982 to 2017, contributing to the country's rapid economic development, increasing its GDP, fixed investment, and regional development. While FDI has brought many benefits, including job creation, technology transfer, and market access, it has also had negative consequences, such as environmental degradation, income inequality, and dependence on foreign capital. To maximize the benefits of FDI and minimize its negative consequences, the Chinese government should implement policies to promote sustainable development, protect the environment, and ensure that the benefits of economic growth are shared equitably among all segments of society.Recommendations:1. Diversify FDI Sources: China should diversify its FDI sources to reduce its dependence on a few major investors and promote a more balanced economic development.2. Promote Sustainable Development: The Chinese government should implement policies to promote sustainable development, including environmental protection, social responsibility, and labor standards.3. Enhance Domestic Industries: China should implement policies to support and develop domestic industries, including small and medium-sized enterprises, to reduce dependence on foreign capital and promote economic self-sufficiency.4. Improve Income Distribution: The government should implement policies to improve income distribution, including progressive taxation, social welfare programs, and labor market regulations, to reduce income inequality and promote social cohesion.5. Foster Cultural Diversity: China should promote cultural diversity and protect its cultural heritage, by implementing policies to support domestic cultural industries and promoting cultural exchange programs with foreign countries.