Question

In accordance with the Bohr's model the quantum number that characterises the earth's revolution around the sun in an orbit of radius $1.5\times 10^{11}m$ with orbital speed $3\times 10^{4}m/s$ (Mass of earth $=6.0\times 10^{24}kg$ ). They belong to

• A. Balmer series
• B. Lyman series
• C. Humbnery series
• D. None of these

Answer 1

Answer: (B)

Given, radius of orbit $r=1.5\times 10^{11}m$
Orbital speed $v=3\times 10^{4}m/s$
Mass of earth $M=6\times 10^{24}kg$
Angular momentum, $mvr=\frac{nh}{2\pi }$
or $n=\frac{2\pi vrm}{h}$ [where, $n$ is the quantum number of the orbit]
$=\frac{2\times 3.14\times 3\times 10^4\times 1.5\times 10^{11}\times 6\times 10^{24}}{6.63\times 10^{-34}}$
$=2.57\times 10^{74}$
or $n=2.6\times 10^{74}$
Thus, the quantum number is $2.6\times 10^{74}$ which is too large.
The electron would jump from $n=1$ to $n=3$.
$E_3=\frac{-13.6}{3^2}=-1.5eV$
So, they belong to Lyman series.