Which of the following statements are correct?

Options

A. If angular momentum the Earth due to its motion around the Sun were quantized according to Bohr's ralation `L = nh//2 pi`, then the quantum number`n` would be the order of `10^(74)`
B. If element with principal quantum number `gt 4` were not allowed in nature , then the number number of possible element would be `64`.
C. Rydberg's constant varies with mass number of the elment.
D. The ratio of the wave number of `H_(a)` lines of Balmer series for hydrogen and that of `H_(a)` line of Balmer series for singly ionized helium is excatly`4`

Answer

A, C

Explanation

Statement (a) is correct. The angular momentum of the earth `(= mr^(2) omega)` has to be equal to `nh//2 pi`. This gives, `n = 2 pi mr^(2) omega//h`. Putting the numierical value of the Earth's mass, redius,and the angular velocity ,we get the given value of `n` .
Statement (b) is incorrect. The maximum number of electrons allowed in an orbit being `2 n^(2)`, the required number is `2 (1^(2) + 2^(2) +3^(2) + 4^(2)) = 60`
Statement ( c) is correct. The `"reduced mass"' of the electron `[mu = Mm//(m + M)]` being dependent on the mass of the nucleus `(M)` , the Rydberg constant also varies with the mass number of the given element.
Statement (d) is incorrect. The ratio is not exctly equal to `4` but sightly difference from `4` because of the depandence of the Rydberg constant on the mass number of the element concerned.