Question
Physics Question on atom structure models
In accordance with the bohr's model the quantum number that characterises the earth revolution around the sun in an orbit of radius 1.5 x 1011 m with orbital speed 3 x 104 m/s is [given mass of the earth = 6 x 1024 kg]
A
8.57x 1064
B
5.98 x 1064
C
2.57 x 1074
D
2.57x 1038
Answer
2.57 x 1074
Explanation
Solution
Radius of the orbit of the Earth around the Sun, r = 1.5 × 1011 m
Orbital speed of the Earth, ν = 3 × 104 m/s
Mass of the Earth, m = 6.0 × 1024 kg
According to Bohr’s model, angular momentum is quantized and given as:
mvr = nh/2π
Where,
h = Planck’s constant = 6.62 × 10−34 Js
n = Quantum number ∴ n = mvr2π/h
= (2πx6x1024x3x104x1.5x1011)/(6.62x10-34)
= 25.61x1073 = 2.6 x 1074
Hence, the quanta number that characterizes the Earth’ revolution is 2.6 × 1074