Explanation:
Given that,
(a) Speed, ![v=6.66\times 10^6\ m/s](https://tex.z-dn.net/?f=v%3D6.66%5Ctimes%2010%5E6%5C%20m%2Fs)
Mass of the electron, ![m_e=9.11\times 10^{-31}\ kg](https://tex.z-dn.net/?f=m_e%3D9.11%5Ctimes%2010%5E%7B-31%7D%5C%20kg)
Mass of the proton, ![m_p=1.67\times 10^{-27}\ kg](https://tex.z-dn.net/?f=m_p%3D1.67%5Ctimes%2010%5E%7B-27%7D%5C%20kg)
The wavelength of the electron is given by :
![\lambda_e=\dfrac{h}{m_ev}](https://tex.z-dn.net/?f=%5Clambda_e%3D%5Cdfrac%7Bh%7D%7Bm_ev%7D)
![\lambda_e=\dfrac{6.63\times 10^{-34}}{9.11\times 10^{-31}\times 6.66\times 10^6}](https://tex.z-dn.net/?f=%5Clambda_e%3D%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B9.11%5Ctimes%2010%5E%7B-31%7D%5Ctimes%206.66%5Ctimes%2010%5E6%7D)
![\lambda_e=1.09\times 10^{-10}\ m](https://tex.z-dn.net/?f=%5Clambda_e%3D1.09%5Ctimes%2010%5E%7B-10%7D%5C%20m)
The wavelength of the proton is given by :
![\lambda_p=\dfrac{h}{m_p v}](https://tex.z-dn.net/?f=%5Clambda_p%3D%5Cdfrac%7Bh%7D%7Bm_p%20v%7D)
![\lambda_p=\dfrac{6.63\times 10^{-34}}{1.67\times 10^{-27}\times 6.66\times 10^6}](https://tex.z-dn.net/?f=%5Clambda_p%3D%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B1.67%5Ctimes%2010%5E%7B-27%7D%5Ctimes%206.66%5Ctimes%2010%5E6%7D)
![\lambda_p=5.96\times 10^{-14}\ m](https://tex.z-dn.net/?f=%5Clambda_p%3D5.96%5Ctimes%2010%5E%7B-14%7D%5C%20m)
(b) Kinetic energy, ![K=1.71\times 10^{-15}\ J](https://tex.z-dn.net/?f=K%3D1.71%5Ctimes%2010%5E%7B-15%7D%5C%20J)
The relation between the kinetic energy and the wavelength is given by :
![\lambda_e=\dfrac{h}{\sqrt{2m_eK}}](https://tex.z-dn.net/?f=%5Clambda_e%3D%5Cdfrac%7Bh%7D%7B%5Csqrt%7B2m_eK%7D%7D)
![\lambda_e=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 9.11\times 10^{-31}\times 1.71\times 10^{-15}}}](https://tex.z-dn.net/?f=%5Clambda_e%3D%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B%5Csqrt%7B2%5Ctimes%209.11%5Ctimes%2010%5E%7B-31%7D%5Ctimes%201.71%5Ctimes%2010%5E%7B-15%7D%7D%7D)
![\lambda_e=1.18\times 10^{-11}\ m](https://tex.z-dn.net/?f=%5Clambda_e%3D1.18%5Ctimes%2010%5E%7B-11%7D%5C%20m)
![\lambda_p=\dfrac{h}{\sqrt{2m_pK}}](https://tex.z-dn.net/?f=%5Clambda_p%3D%5Cdfrac%7Bh%7D%7B%5Csqrt%7B2m_pK%7D%7D)
![\lambda_p=\dfrac{6.63\times 10^{-34}}{\sqrt{2\times 1.67\times 10^{-27}\times 1.71\times 10^{-15}}}](https://tex.z-dn.net/?f=%5Clambda_p%3D%5Cdfrac%7B6.63%5Ctimes%2010%5E%7B-34%7D%7D%7B%5Csqrt%7B2%5Ctimes%201.67%5Ctimes%2010%5E%7B-27%7D%5Ctimes%201.71%5Ctimes%2010%5E%7B-15%7D%7D%7D)
![\lambda_p=2.77\times 10^{-13}\ m](https://tex.z-dn.net/?f=%5Clambda_p%3D2.77%5Ctimes%2010%5E%7B-13%7D%5C%20m)
Hence, this is the required solution.
Answer:
Restoring force of the spring is 50 N.
Explanation:
Given that,
Spring constant of the spring, k = 100 N/m
Stretching in the spring, x = 0.5 m
We need to find the restoring force of the spring. It can be calculated using Hooke's law as "the force on a spring varies directly with the distance that it is stretched".
![F=kx](https://tex.z-dn.net/?f=F%3Dkx)
![F=100\ N/m\times 0.5\ m](https://tex.z-dn.net/?f=F%3D100%5C%20N%2Fm%5Ctimes%200.5%5C%20m)
F = 50 N
So, the restoring force of the spring is 50 N. Hence, this is the required solution.
Voltage, V = IR
Where I is current in Ampere, R is Resistance in Ohms.
V = 9A * 43 Ω
V = 387 V
Answer:
Tides on our planet are caused by the gravitational pull of the Moon and Sun. Earth's oceans "bulge out" because the Moon's gravity pulls a little harder on one side of our planet (the side closer to the Moon) than it does on the other. The Sun's gravity raises tides, too, but lunar tides are twice as big.