Answer:
a) 4.04*10^-12m
b) 0.0209nm
c) 0.253MeV
Explanation:
The formula for Compton's scattering is given by:
![\Delta \lambda=\lambda_f-\lambda_i=\frac{h}{m_oc}(1-cos\theta)](https://tex.z-dn.net/?f=%5CDelta%20%5Clambda%3D%5Clambda_f-%5Clambda_i%3D%5Cfrac%7Bh%7D%7Bm_oc%7D%281-cos%5Ctheta%29)
where h is the Planck's constant, m is the mass of the electron and c is the speed of light.
a) by replacing in the formula you obtain the Compton shift:
![\Delta \lambda=\frac{6.62*10^{-34}Js}{(9.1*10^{-31}kg)(3*10^8m/s)}(1-cos132\°)=4.04*10^{-12}m](https://tex.z-dn.net/?f=%5CDelta%20%5Clambda%3D%5Cfrac%7B6.62%2A10%5E%7B-34%7DJs%7D%7B%289.1%2A10%5E%7B-31%7Dkg%29%283%2A10%5E8m%2Fs%29%7D%281-cos132%5C%C2%B0%29%3D4.04%2A10%5E%7B-12%7Dm)
b) The change in photon energy is given by:
![\Delta E=E_f-E_i=h\frac{c}{\lambda_f}-h\frac{c}{\lambda_i}=hc(\frac{1}{\lambda_f}-\frac{1}{\lambda_i})\\\\\lambda_f=4.04*10^{-12}m +\lambda_i=4.04*10^{-12}m+(0.0169*10^{-9}m)=2.09*10^{-11}m=0.0209nm](https://tex.z-dn.net/?f=%5CDelta%20E%3DE_f-E_i%3Dh%5Cfrac%7Bc%7D%7B%5Clambda_f%7D-h%5Cfrac%7Bc%7D%7B%5Clambda_i%7D%3Dhc%28%5Cfrac%7B1%7D%7B%5Clambda_f%7D-%5Cfrac%7B1%7D%7B%5Clambda_i%7D%29%5C%5C%5C%5C%5Clambda_f%3D4.04%2A10%5E%7B-12%7Dm%20%2B%5Clambda_i%3D4.04%2A10%5E%7B-12%7Dm%2B%280.0169%2A10%5E%7B-9%7Dm%29%3D2.09%2A10%5E%7B-11%7Dm%3D0.0209nm)
c) The electron Compton wavelength is 2.43 × 10-12 m. Hence you can use the Broglie's relation to compute the momentum of the electron and then the kinetic energy.
![P=\frac{h}{\lambda_e}=\frac{6.62*10^{-34}Js}{2.43*10^{-12}m}=2.72*10^{-22}kgm\\](https://tex.z-dn.net/?f=P%3D%5Cfrac%7Bh%7D%7B%5Clambda_e%7D%3D%5Cfrac%7B6.62%2A10%5E%7B-34%7DJs%7D%7B2.43%2A10%5E%7B-12%7Dm%7D%3D2.72%2A10%5E%7B-22%7Dkgm%5C%5C)
![E_e=\frac{p^2}{2m_e}=\frac{(2.72*10^{-22}kgm)^2}{2(9.1*10^{-31}kg)}=4.06*10^{-14}J\\\\1J=6.242*10^{18}eV\\\\E_e=4.06*10^{-14}(6.242*10^{18}eV)=0.253MeV](https://tex.z-dn.net/?f=E_e%3D%5Cfrac%7Bp%5E2%7D%7B2m_e%7D%3D%5Cfrac%7B%282.72%2A10%5E%7B-22%7Dkgm%29%5E2%7D%7B2%289.1%2A10%5E%7B-31%7Dkg%29%7D%3D4.06%2A10%5E%7B-14%7DJ%5C%5C%5C%5C1J%3D6.242%2A10%5E%7B18%7DeV%5C%5C%5C%5CE_e%3D4.06%2A10%5E%7B-14%7D%286.242%2A10%5E%7B18%7DeV%29%3D0.253MeV)
Use Factor-Label Method:
8miles 63360 inches
---------- X --------------------- X
1 1 mile
2.54cm 1 meter
X ------------ X ---------------- X
1 inch 100 cm
1 km
----------------- = 12.87 km
1000meters
8 miles = 12.87 km
King Arthur's knights use a catapult to launch a rock from their vantage point on top of the castle wall, 14 m above the moat. The rock is launched at a speed of 27 m/s and an angle of 32degrees above the horizontal.
Answer:
L/T^2.
Explanation:
Dimensional analysis is defined as the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, temperature etc.) and units of measure (such as miles vs. kilometers, pounds vs. kilograms etc.).
F = m * a
kg(m/s^2) = kg * a
In dimensions,
a = L/T^2.
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