Question

The energy of a photon is given as $3.03\times {10}^{-19}\mathrm{J}/\mathrm{atom}$. The wavelength of the photon is :

• A. $6.56\mathrm{nm}$
• B. $65.6\mathrm{nm}$
• C. $0.656\mathrm{nm}$
• D. $656\mathrm{nm}$

Answer 1

The correct option is D

$656\mathrm{nm}$

Step 1 : Wavelength :

1. Wavelength is defined as the distance between corresponding points of two consecutive waves.
2. It is denoted by $\lambda$.
3. The SI unit of wavelength is meter.

Step 2 : Calculation :

We have given that the energy of photon is $3.03\times {10}^{-19}\mathrm{J}/\mathrm{atom}$.

The formula to calculate wavelength is :

$\mathrm{\lambda }=\frac{\mathrm{hc}}{\mathrm{E}}$

Where, $\lambda$ = wavelength, $\mathrm{h}$= Plank's constant = $6.626\times {10}^{-34}\mathrm{Js}$, $\mathrm{c}$ = $3\times {10}^8\mathrm{m}/\mathrm{s}$.

Substituting the values in formula :

$\lambda =\frac{(6.626\times {10}^{-34}\mathrm{Js})\times (3\times {10}^8\mathrm{m}/\mathrm{s})}{3.03\times {10}^{-19}\mathrm{J}/\mathrm{atom}}$

$\mathrm{\lambda }=656\mathrm{nm}$

Hence option $\left(\mathrm{D}\right)$ is correct and rest stands incorrect.