Question

Calculate the energy in $\text{eV}$ of $1$ mole of photons having a wavelength of $331\text{nm}$.

• A. $5.37\text{eV}$
• B. $6.88\text{eV}$
• C. $2.58\text{eV}$
• D. $3.75\text{eV}$

Answer 1

The correct option is D $3.75\text{eV}$

According to Planck's Quantum theory,
$E=hv=\frac{hc}{\lambda }$
where $h=$ Planck's constant
$v$ is the frequency of the photon
$\lambda$ = wavelength of the photon $=331\text{nm}=331\times {10}^{-9}\text{m}$
So, $E=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{331\times {10}^{-9}}$
$E=6.0\times {10}^{-19}$ J
We know, $1\text{eV}=1.6\times {10}^{-19}\text{J}$
$\therefore E=\frac{6.0\times {10}^{-19}}{1.6\times {10}^{-19}}=3.75\text{eV}$