Question

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

• A. $\frac{2}{3}$nm
• B. $\frac{20}{3}$nm
• C. $\frac{4}{3}$nm
• D. $\frac{40}{3}$nm
• E. $\frac{3}{20}$nm

Answer 1

Answer: (B)

$\frac{20}{3}$nm

Given,

$m_e=$mass of electron

$=9\times {10}^{-31}kg$

$v_e=1.1\times {10}^{5}m/s$

Momentum, $p=m_e{v}_e$

$p=9\times {10}^{-31}\times 1.1\times {10}^5$

$=9.9\times {10}^{-26}kgm/s$

From de-Broglie waves

$\lambda =\frac{h}{p}=\frac{6.6\times {10}^{-34}}{9.9\times {10}^{-26}}m$

$=\frac{2}{3}\times {10}^{-8}m$

$=\frac{20}{3}\times {10}^{-9}m=\frac{20}{3}nm$