Question

Find the (a) Maximum frequency and (b) Minimum wave length of X -rays produced by 30 ke V.

Answer 1

Potential of electrons, $v=30$kv

$=3\times {10}^4$v

Energy of electrons, $E=3\times {10}^4$ eV

$(e=1.6\times {10}^{-19}c)$ charge on electrons

a) $E=hv$

$E=$ Energy of electrons,

$h=$ Planck's constant

$=6.626\times {10}^{-34}$J-S

$v=$Maximum frequency produced by x-rays.

$v=\frac{E}{h}$

$=\frac{3\times {10}^4\times 1.6\times {10}^{-19}}{6.626\times {10}^{-34}}$

$=7.24\times {10}^{18}$Hz

b) The minimum wavelength produced by x-rays

$A=\frac{c}{v}$ ($c=$ speed of light)

$=\frac{3\times {10}^8}{7.24\times {10}^{18}}=4.14\times {10}^{-11}m=0.0414$nm.