Question

the radius of first permitted bohr Orbit for the electron in a hydrogen atom = 0.51 angstrom and its ground state energy = -13.6 electron volt if the electron in the hydrogen atom is replaced by Muon then the first bohr radius and ground state energy will be ​

Answer 1

Explanation:

substitute formula and get the answer. see the image

Answer 2

The first bohr radius is rm = 2.46 x 10^-13 m and ground state energy will be Em = -2.8 KeV

Explanation:

Given data:

• Bohr orbit = 0.51 angstrom
• Ground state energy = - 13.6 eV

Solution:

re = Ke^2 / meV

rm = Ke^2 / 201 meV

rm = 0.51 / 207 x 10^-10

rm = 2.46 x 10^-13 m

Ee = KZe^2 / 2 (0.5)

13.6 x 2 x 0.51 A = KZe^2

Em = KZe^2 / 2 rm

Em = 13.6 x 2 x 0.51 x 10^-10 / 2 x 2.46 x 10^-13

Em = -13.6 x 0.51 x 10^3 / 2.46

Em = -2.8 KeV

Hence the first bohr radius is rm = 2.46 x 10^-13 m and ground state energy will be Em = -2.8 KeV