Answer to Question #101924 in Mechanics | Relativity for jude

Question

Complete the wavelength of the light of the following and comment on what will happen to the light in these scenarios:
a) Light passes through two slits 2.7 micrometers apart and shines on a screen. The first order maxima occurs at angle 9.5 degrees.
b) Light is incident on a metal with work function 2.28eV. The maximum kinetic energy of photoelectrons is 0.51eV.

Answer 1

Given that,

the distance between the two slits $d=2.7\times 10^{-6}m$

first order maxima $\theta=9.5$

a) We know that $\sin\theta=1.22\dfrac{\lambda}{d}$

$\Rightarrow \lambda=\dfrac{d\sin\theta}{1.22}=\dfrac{2.7\times10^{-6}\sin 9.5^\circ m}{1.22}$

$\Rightarrow \lambda=\dfrac{2.7\times0.16\times10^{-6}}{1.22}=0.35\times 10^{-6}m$

b)

$\dfrac{mv^2}{2}=\dfrac{hc}{\lambda}-\phi$

$\Rightarrow 0.51eV=\dfrac{hc}{\lambda}-2.28eV$

$\Rightarrow \dfrac{hc}{\lambda}=0.51eV+2.28eV=2.79eV$

$\Rightarrow \lambda=\dfrac{6.6\times 10^{-34}\times3\times10^{3}}{2.79\times1.6\times10^{-19}}$

$\Rightarrow \lambda=4.43\times10^{-12}m$