Electrons are ejected from a metallic surface with speeds ranging up to 4.7 x 10

Question

Electrons are ejected from a metallic surface with speeds ranging up to 4.7 x 105 m/s wh light with a wavelength of 615 nm is used. en (a) What is the work function of the surface? eV (b) What is the cutoff frequency for this surface? Hz Need Help? Read It -3 points SerPSE9 40. PO33 X-rays having an energy of 330 keV undergo Compton scattering from a target. The scattered rays are detected at 37.0° relative to the incident rays. (a) Find the Compton shift at this angle. (b) Find the energy of the scattered x-ray. ke (c) Find the energy of the recoiling electron. ke Need Help? Read It -2 points SerPSE9 40. PO39 (a) Calcul ate the momentum of a photon whose wavelength is 5.03 x 10 m. kg m/s (b) Find the speed of a electron having the same momentum as the photon in part (a). km/s Need Help? Read It

Explanation / Answer

1)

a)

electron speed v=4.7*10^5 m/sec

wavelength lambda=615 nm

by using Einstein's photoelectric equation,

h*f= W+K.E

hc/lambda=w+1/2*m*v^2

w =(hc/lambda)-1/2*m*v^2

= ((6.626*10^-34*3*10^8)/(615*10^-9)) -(1/2*9.109*10^-31*4.7^2*10^10)

= 2.226*10^-19 j

= 1.39 ev

b)

w=h*fo

cutt of frequency fo=w/h

=(2.226*10^-19)/(6.626*10^-34)

=3.36*10^14 Hz

2)

incident energy E=330 kev

theta=37 degrees

a)

compton shift dL=(h/mo*C)*(1-cos(theta))

=((6.628*10^-34)/(9.1*10^-31*3*10^8))*(1-cos(37))

=5.6953*10^-13 m

=0.057 Angsrom

b)

E=hc/L

L=hc/E

=(6.62*10^-34*3*10^8)/(330*10^3*1.6*10^-19)

=3.7613*10^-12 m

incidant wavelength L =0.00376 nm

scattered wavelength L'= dL+L1

L2=(5.6953*10^-13)-(3.7613*10^-12)

=4.248*10^-12 m

=0.00424 nm

now,

enrgy of the scattered ray E= hc/L'

=(6.62*10^-34*3*10^8)/(4.248*10^-12)

=4.67*10^-14 j

=2.918*10^5 ev

c)

kinetic enrgy of electron is,

K.E=(330*10^3) - (2.918*10^5)

=38200 ev

=0.382*10^5 ev

3)

a)

wavelength lambda=5.03*10^-7 m

momentum P=h/lambda

=(6.626*10^-34)/(5.03*10^-7)

=1.32*10^-27 kg*m/Sec

b)

P=1.32*10^-27 kg*m/sec^2

P=m*v

v=p/m

=(1.32*10^-27)/(9.1*10^-31)

=1.45*10^3 m/sec

1.45 km/sec

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