Question

What are the average distance and the most probable distance of an electron from the nucleus in the $1\mathrm{s}$ orbital of a hydrogen atom? (${\mathrm{a}}_0=$the radius of the first Bohr orbit)

Answer 1

Most probable distance:

• The most probable distance is the range of the orbit in which the electron is most likely to be.
• ${\mathrm{v}}_{mps}=\sqrt{\frac{2\mathrm{RT}}{\mathrm{M}}}$
• The most likely distances of an electron out from the nucleus in a hydrogen atom's $1\mathrm{s}$ orbital is $a_0$.
• $a_0$ has a value of $0.529\mathrm{A}°$.
• As a result, the most probable distances of an electron from the nucleus in a hydrogen atom's $1\mathrm{s}$ orbital is $0.529\mathrm{A}°$.

The average distance:

• the average distance is the expected value of the length of an electron out from the nucleus.
• ${\mathrm{v}}_{\mathrm{av}}=\sqrt{\frac{8\mathrm{RT}}{\mathrm{\pi M}}}$
• The average distance of an electron out from the nucleus in a hydrogen atom's $1\mathrm{s}$ orbital is $1.5a_0$.
• $a_0$ has a value of $0.529\mathrm{A}°$.
• As a result, the average distance of an electron from the nucleus in a hydrogen atom's $1\mathrm{s}$ orbital is $0.794\mathrm{A}°$