Question

What wavelength must electromagnetic radiation have if a photon in the beam has the same momentum as an electron moving with a speed $1.1 \times 10^5m / s $ (Planck’s constant = $6.6 \times 10^{-34} \, J-s$ , rest mass of electron = $ 9 \times 10^{-31} \, kg$ ?

• A. 2/3 nm
• B. 20/3 nm
• C. 4/3 nm
• D. 40/3 nm
• E. 3/20 nm

Answer 1

Answer: (B)

Given,
$m_{e}=$ mass of electron
$=9 \times 10^{-31}\, kg$
$=101 \times 10^{5} \,m / s$
momentum, $p=m_{e} V_{e}$
$p =9 \times 10^{-31} \times 1.1 \times 10^{5} $
$=9.9 \times 10^{-26}\, kg - m / s$
From de-Broglie waves
$ \lambda =\frac{h}{p}=\frac{6.6 \times 10^{-34}}{9.9 \times 10^{-26}} m $
$=\frac{2}{3} \times 10^{-8}\, m $
$=\frac{20}{3} \times 10^{-9} \,m =\frac{20}{3} \,nm $