Question

The number of revolutions made by an electron per second in the third orbit of hydrogen atom is (in the first orbit of hydrogen atom, velocity = and radius = 0.53 å)

Answer 1

Answer:

The number of revolutions made by an electron per second in the third orbit of hydrogen atom is 2.40758 x 10^14 cycles /sec

Explanation:

Answer 2

at first, we have to find velocity of electron and then radius of orbit in which electron revolves around the nucleus.

from Bohr's theory,

$v_n=2.165\times10^6\frac{Z}{n}$m/s

where Z is atomic number and n is orbit number.

for 3rd orbit of H-atom,

Z = 1 and n = 3

so, v = 2.165 × 10^6 × 1/3

= 0.7217 × 10^6 m/s

again, radius of nth orbit, $r_n=0.53\frac{n^2}{Z}$A°

for 3rd orbit for H-atom. n = 3 and z = 1

= 0.53 × 3²/1 A°

= 4.77 × 10^-10m

now, number of revolution made by an electron per second , f = v/2πr

= 0.7217 × 10^6/(2 × 3.14 × 4.77 × 10^-10

= 0.024 × 10^16 Hz

= 2.4 × 10¹⁴ Hz