Question

The first ionization energy of a nitrogen atom is 2.32 aJ (attojoules). What is the frequency and wavelength, in nanometers, of photons capable of just ionizing nitrogen atoms?

Answer 1

Explanation:

It is given that,

The ionization energy of a nitrogen atom, $E=2.32\ aJ$

aJ is attpjoules. $1\ aJ=10^{-18}\ J$

$E=2.32\times 10^{-18}\ J$

The energy of an atom is given by :

$E=h\times f$

f is the frequency of the photons

$f=\dfrac{E}{h}$

$f=\dfrac{2.32\times 10^{-18}}{6.67\times 10^{-34}}$

$f=3.47\times 10^{15}\ Hz$

Also, $E=\dfrac{hc}{\lambda}$

$\lambda=\dfrac{hc}{E}$

$\lambda=\dfrac{6.67\times 10^{-34}\times 3\times 10^8}{2.32\times 10^{-18}}$

$\lambda=8.62\times 10^{-8}\ m$

Hence, this is the required solution.