State the Following statement as statements as TRUE and FALSE.
a. The redius of nth Bohr is proporitional to `n^(2)`.
b. The total energy of electron in the nth orbit is inversely proporitional to `n^(2)`.
c. The time period revolution of electron in the nth orbit is directly proporitional to `n^(2)`.
d. The kinetic energy of electron is double of its potential energy with a negative sign.
e. Velocity of electron in an atom is independent of its mass.
f. Only balmer series of hydrogen atom lines in the visible range.
g. The angular momentum of an electron revolving in the first orbit of hydrogen is equal to that in first orbit of helium.
h. The binding energy of decuterium atom is more than that of hydrogen atom.
i Lyman series of hydrogen atom lines in the infrared region.

Explanation

a. True , `r = 0.53 (Z^(2))/(n^(2)) Å`
b. True `E_(n) = - 13.6 (Z^(2))/(n^(2)) (e V)`
c.True `T = (2 pi r)/(v) implies Tprop (n^2)/(Z) - (n)/(Z) prop (n^2)/(Z) `
Since r prop `n^(2)` and `v prop (1)/(n)` therefore `T prop n^(2)`
d. false . `U = - 2 K`
e. True `v = (2 pi k Ze^(2))/(nh)`
f. True
g. True, the expression `mvr = nh//2 pi` is independent of the atomic number `Z` .
h. True. The value of Rydberg constant for deuterium is more than that of hydrogen . Therefore, ground state energy level for deuterium is lower than that of hydrogen.
i False. Lyman series lies in the ultraviolet region.