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 $h v=h c / \lambda$
$=\frac{6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s} \times 3.0 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}}{300 \times 10^{-9} \mathrm{~m}}$
$=6.626 \times 10^{-19} \mathrm{~J}$
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
$=(3.99-1.68) 10^{5} \mathrm{~J} \mathrm{~mol}^{-1}$
$=2.31 \times 10^{5} \mathrm{~J} \mathrm{~mol}^{-1}$