Question

The radius of the 4th orbit of the electron will be smaller than its 8th orbit by a factor of.?​

Answer 1

Answer:

1/4 [or 0.25]

Explanation:

Radius of the nth Bohr orbit for a hydrogen atom is given by:

rₙ = 0.529n² Å

where 'n' stands for the principle quantum number of the electron [i.e. , the orbit in which the electron is spinning].

So,

Radius of 4th orbit of electron:

r₄ = 0.529 × 4² Å ............................[equation 1]

Radius of 8th orbit of electron:

r₈ = 0.529 × 8² Å ............................[equation 2]

Dividing equations 1 and 2,

r₄ / r₈ = (0.529 × 4²) Å / (0.529 × 8²) Å

r₄ / r₈ = 4² / 8²

r₄ / r₈ = 16 / 64

r₄ / r₈ = 1 / 4

=> r₄ = (1 / 4) r₈

Hence, the radius of the 4th orbit of the electron will be smaller than its 8th orbit by a factor of 1 / 4 , i.e. , the radius of the 4th orbit of the electron will be 1 / 4 times smaller than its 8th orbit.