Question

The ratio of the difference between $1$st and $2$nd Bohr orbits energy to that between $2$nd and $3$rd orbits energy is:

• A. $1/2$
• B. $1/3$
• C. $27/5$
• D. $5/27$

Answer 1

The correct option is C $27/5$

The ratio of the difference between 1st and 2nd Bohr orbits energy to that between 2nd and 3rd orbits energy is $\frac{27}{5}$
For a hydrogen atom, the energies that an electron can have are given by the expression, $E=-\frac{13.58}{n^2}eV$, where n is an integer.
For first energy level,
$E_1=-\frac{13.58}{1^2}eV=-13.58eV$
For second energy level,
$E_2=-\frac{13.58}{2^2}eV=-3.395eV$
The difference $E_2-E_1=-3.395eV-(-13.58eV)=10.19eV$
For second energy level,
$E_2=-\frac{13.58}{2^2}eV=-3.395eV$
For third energy level,
$E_3=-\frac{13.58}{3^2}eV=-1.51eV$
The difference $E_3-E_2=-1.51eV-(-3.395eV)=1.89eV$
The ratio of the difference between 1st and 2nd Bohr orbits energy to that between 2nd and 3rd orbits energy is $\frac{10.19eV}{1.89eV}=\frac{27}{5}$