Answer:
Explanation:the atom consists of a tiny nucleus at its center which is surrounded by a moving electrons. The nucleus contains a positively charged proton equal in size with the negatively charged electrons . The nucleus also may contain neutrons which have the same mass with the protons but no charge is neutral.
Answer:
Part A:
The proton has a smaller wavelength than the electron.
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Part B:
The proton has a smaller wavelength than the electron.
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Explanation:
The wavelength of each particle can be determined by means of the De Broglie equation.
(1)
Where h is the Planck's constant and p is the momentum.
(2)
Part A
Case for the electron:
![\lambda = \frac{6.624x10^{-34} J.s}{(9.11x10^{-31}Kg)(6.55x10^{6}m/s)}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B6.624x10%5E%7B-34%7D%20J.s%7D%7B%289.11x10%5E%7B-31%7DKg%29%286.55x10%5E%7B6%7Dm%2Fs%29%7D)
But ![J = Kg.m^{2}/s^{2}](https://tex.z-dn.net/?f=J%20%3D%20Kg.m%5E%7B2%7D%2Fs%5E%7B2%7D)
![\lambda = \frac{6.624x10^{-34}Kg.m^{2}/s^{2}.s}{(9.11x10^{-31}Kg)(6.55x10^{6}m/s)}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B6.624x10%5E%7B-34%7DKg.m%5E%7B2%7D%2Fs%5E%7B2%7D.s%7D%7B%289.11x10%5E%7B-31%7DKg%29%286.55x10%5E%7B6%7Dm%2Fs%29%7D)
![\lambda = 1.10x10^{-10}m](https://tex.z-dn.net/?f=%5Clambda%20%3D%201.10x10%5E%7B-10%7Dm)
Case for the proton:
![\lambda = \frac{6.624x10^{-34}Kg.m^{2}/s^{2}.s}{(1.67x10^{-27}Kg)(6.55x10^{6}m/s)}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B6.624x10%5E%7B-34%7DKg.m%5E%7B2%7D%2Fs%5E%7B2%7D.s%7D%7B%281.67x10%5E%7B-27%7DKg%29%286.55x10%5E%7B6%7Dm%2Fs%29%7D)
![\lambda = 6.05x10^{-14}m](https://tex.z-dn.net/?f=%5Clambda%20%3D%206.05x10%5E%7B-14%7Dm)
Hence, the proton has a smaller wavelength than the electron.
<em>Part B </em>
For part b, the wavelength of the electron and proton for that energy will be determined.
First, it is necessary to find the velocity associated to that kinetic energy:
![KE = \frac{1}{2}mv^{2}](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7Dmv%5E%7B2%7D)
![2KE = mv^{2}](https://tex.z-dn.net/?f=2KE%20%3D%20mv%5E%7B2%7D)
(3)
Case for the electron:
![v = \sqrt{\frac{2(7.89x10^{-15}J)}{9.11x10^{-31}Kg}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B2%287.89x10%5E%7B-15%7DJ%29%7D%7B9.11x10%5E%7B-31%7DKg%7D%7D)
but
![v = \sqrt{\frac{2(7.89x10^{-15}kg \cdot m^{2}/s^{2})}{9.11x10^{-31}Kg}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B2%287.89x10%5E%7B-15%7Dkg%20%5Ccdot%20m%5E%7B2%7D%2Fs%5E%7B2%7D%29%7D%7B9.11x10%5E%7B-31%7DKg%7D%7D)
![v = 1.316x10^{8}m/s](https://tex.z-dn.net/?f=v%20%3D%201.316x10%5E%7B8%7Dm%2Fs)
Then, equation 2 can be used:
![\lambda = 5.525x10^{-12}m](https://tex.z-dn.net/?f=%5Clambda%20%3D%205.525x10%5E%7B-12%7Dm)
Case for the proton :
![v = \sqrt{\frac{2(7.89x10^{-15}J)}{1.67x10^{-27}Kg}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B2%287.89x10%5E%7B-15%7DJ%29%7D%7B1.67x10%5E%7B-27%7DKg%7D%7D)
But ![1J = kg \cdot m^{2}/s^{2}](https://tex.z-dn.net/?f=1J%20%3D%20kg%20%5Ccdot%20m%5E%7B2%7D%2Fs%5E%7B2%7D)
![v = \sqrt{\frac{2(7.89x10^{-15}kg \cdot m^{2}/s^{2})}{1.67x10^{-27}Kg}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B2%287.89x10%5E%7B-15%7Dkg%20%5Ccdot%20m%5E%7B2%7D%2Fs%5E%7B2%7D%29%7D%7B1.67x10%5E%7B-27%7DKg%7D%7D)
![v = 3.07x10^{6}m/s](https://tex.z-dn.net/?f=v%20%3D%203.07x10%5E%7B6%7Dm%2Fs)
Then, equation 2 can be used:
![\lambda = \frac{6.624x10^{-34}Kg.m^{2}/s^{2}.s}{(1.67x10^{-27}Kg)(3.07x10^{6}m/s)}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B6.624x10%5E%7B-34%7DKg.m%5E%7B2%7D%2Fs%5E%7B2%7D.s%7D%7B%281.67x10%5E%7B-27%7DKg%29%283.07x10%5E%7B6%7Dm%2Fs%29%7D)
Hence, the proton has a smaller wavelength than the electron.
Answer:
-5 m/s
Explanation:
The linear velocity of B is equal and opposite the linear velocity of E.
vB = -vE
vB = -ωE rE
10 m/s = -ωE (12 m)
ωE = -0.833 rad/s
The angular velocity of E is the same as the angular velocity of D.
ωE = ωD
ωD = -0.833 rad/s
The linear velocity of Q is the same as the linear velocity of D.
vQ = vD
vQ = ωD rD
vQ = (-0.833 rad/s) (6 m)
vQ = -5 m/s
The momentum of ball is given by:
Since both have the same momentum, we have:
Number 3If you notice any mistake in my english, please let me know, because i am not native.