Question

When electromagnetic radiation of wavelength $300\mathrm{nm}$ falls on the surface of sodium, electrons are emitted with a kinetic energy of $1.68\times 10^5\mathrm{J}{\mathrm{mol}}^{-1}$. What is the minimum energy needed to remove an electron from sodium?

• A. $3.34\times 10^{-5}\mathrm{J}{\mathrm{mol}}^{-1}$
• B. $4.10\times 10^{-3}\mathrm{J}{\mathrm{mol}}^{-1}$
• C. $8.15\times 10^{-5}\mathrm{J}{\mathrm{mol}}^{-1}$
• D. $2.31\times 10^5\mathrm{J}{\mathrm{mol}}^{-1}$

Answer 1

Answer: (D)

The energy $(E)$ of a $300\mathrm{nm}$ photon is given by $hv=hc/\lambda$
$=\frac{6.626\times 10^{-34}\mathrm{J}\mathrm{s}\times 3.0\times 10^8\mathrm{m}{\mathrm{s}}^{-1}}{300\times 10^{-9}\mathrm{m}}$
$=6.626\times 10^{-19}\mathrm{J}$
The energy of one mole of photons
$=6.626\times 10^{-19}\mathrm{J}\times 6.022\times 10^{23}{\mathrm{mol}}^{-1}$
$=3.99\times 10^5\mathrm{J}{\mathrm{mol}}^{-1}$
The minimum energy needed to remove a mole of electrons from sodium
$=(3.99-1.68)10^5\mathrm{J}{\mathrm{mol}}^{-1}$
$=2.31\times 10^5\mathrm{J}{\mathrm{mol}}^{-1}$