Question

The energy associated with the first orbit in the hydrogen atom is -2.17 x 10-18 J aton What is the energy associated with the fifthorbit ? Calculate radius of Bohr's fifth orbit of Hyrogen atom.​

Answer 1

Answer:

$\displaystyle{E_5=-8.68\times10^{-20} \ J/atom}\\\\\displaystyle{r_5=1.323 \ nm}$

Explanation:

1.  

Energy of nth orbit in H atom is given by

$\displaystyle{E_n=-\dfrac{2.17\times10^{-18}}{n^2} \ J/atom}$

Energy associated with 5th orbit is as ;  

$\displaystyle{E_5=-\dfrac{2.17\times10^{-18}}{5^2} \ J/atom}\\\\\\\displaystyle{E_5=-\dfrac{2.17\times10^{-18}}{25} \ J/atom}\\\\\\\displaystyle{E_5=-8.68\times10^{-20} \ J/atom}$

2.

Radius of Bohr's nth orbit is given by as ;

$\displaystyle{r_n=0.0529 \ n^2 \ nm}$

Radius for n = 5 is ;  

$\displaystyle{r_5=0.0529\times 5^2 \ nm}\\\\\displaystyle{r_5=0.0529\times25 \ nm}\\\\\displaystyle{r_5=1.323 \ nm}$

Thus we get answer .  

Answer 2

Energy of an atom in an orbit = -13.6eV÷n²

n is the principal quantum number.

in the first orbit , the energy is (-13.6×1.6×10^-19)÷1²

so , the energy is -2.18×10^-18 J.

so in the fifth orbit, energy = (-13.6×1.6×10^-19)÷5²

energy = -8.704×10^-20 J

2) Bohr radius = 0.53×10^-10× n²

in fifth orbit ,

Bohr radius = (0.53×10^-10)×5²

Bohr radius = 1.325×10^-9 .