(i) The energy associated with the first orbit in the hydrogen atom is

1.	(i) The energy associated with the first orbit in the hydrogen atom is -2.18 × 10-18 atom-1 . What is the energy associated with the fourth orbit? (ii) Calculate the radius of Bohr's third orbit for hydrogen atom.
Answer» (i) E = -2.18 x 10^-18 x \(\frac{z^2}{n^2}J\) atom^-1 For H − atom, z = 1 value of n for fourth orbit = 4 \(\therefore\) E = -2.18 x 10^-18\(\frac{(1)^2}{(4)^2}\) = \(\frac{-2.18\times10^{-18}}{16}\) = -0.136 x 10^-18 =-1.36 x 10^-19 J (ii) Radius of third orbit for H-atom r_n = \(\frac{52.9n^2}{z}\) r₃ = \(\frac{52.9\times(3)^2}{1}\) = 52.9 × 9 = 476.1 pm

(i) The energy associated with the first orbit in the hydrogen atom is -2.18 × 10-18 atom-1 . What is the energy associated with the fourth orbit? (ii) Calculate the radius of Bohr's third orbit for hydrogen atom.

Answer»

(i) E = -2.18 x 10^-18 x \(\frac{z^2}{n^2}J\) atom^-1

For H − atom, z = 1

value of n for fourth orbit = 4

\(\therefore\) E = -2.18 x 10^-18\(\frac{(1)^2}{(4)^2}\)

= \(\frac{-2.18\times10^{-18}}{16}\)

= -0.136 x 10^-18

=-1.36 x 10^-19 J

(ii) Radius of third orbit for H-atom

r_n = \(\frac{52.9n^2}{z}\)

r₃ = \(\frac{52.9\times(3)^2}{1}\)

= 52.9 × 9

= 476.1 pm