Question

A photon and an electron both have wavelength $1\hat{A}$ . The ratio of energy of photon to that of electron is

• A. $1$
• B. $0.012$
• C. $82.7$
• D. ${10}^{-10}$

Answer 1

The correct option is C $82.7$

The Energy of the Photon is to be calculated by the formula

$E=hc/\lambda$

and The Energy of the Electron is to be calculated by the formula

$K=p^2/2m$ where $p=h/\lambda$

The Energy of Photon is $E=(6.626\times {10}^{-34}\times 3\times {10}^8)/\left({10}^{-10}\right)Joule$

$E=19.878\times {10}^{-16}Joule$

The Energy of electron is $E=\left(\right(6.626\times {10}^{-34}{)}^2\left)/\right(({10}^{-10}{)}^2\times 2\times 9.1\times {10}^{-31})Joule=2.412\times {10}^{-17}Joule$

Now the Ratio of Energy of Photon to Energy of Electron = $82.481\approx 82.7$