Question

How far from the nucleus in angstroms (1 angstrom = 1 × 10–10 m) is the electron in a hydrogen atom if it has an energy of –8.72 × 10–20 J?

Answer 1

Bohr's model of atom postulated that the electrons revolves around the nucleus only in those orbits which have fixed energy and do not lose energy while revolving in them.

According to Bohr's model, the energy at infinite distance is taken to be zero and as it approaches the atom, it starts becoming more negative.

The $n^{th}$ shell of electrons is calculated by

$n^2 = \frac{kZ^2}{E_n}$

Here

E_n = Energy at $n^{th}$ level

k = Constant

n = Number of shell

Z = Atomic number of the element

Replacing we have that

$n^2 = \frac{-(2.179*10^{-18}J)(1)^2}{-8.72*10^{-20}J}$

$n = 24.98$

$n \approx 25$

Thus

$n = \pm 5$

Since number of shell cannot be negative we have that n = 5

Now the distance of electron from nucleus is given according to relation

$r = (0.529)(n^2)$

$r = (0.529)(5^2)$

$r = 13.225 \AA$

Therefore the distance of electron from nucleus is 13.225A