Q. In hydrogen and hydrogen-like atoms, the ratio of E* _{4n}*– E

*and E*

_{2n}*– E*

_{2n}*varies with atomic number*

_{n}*z*and principal quantum number

*n*as

(a) Z^{2}/n^{2}

(b) Z^{4}/n^{4}

(c) Z/n

(d) None of these

Ans: (d)

Sol: E_{4n} − E_{2n} = (−13.6Z^{2}/(4n)^{2}) – (−13.6Z^{2}/(2n)^{2})

= 13.6Z^{2}/4n^{2} – 13.6Z^{2}/16n^{2} ……..(i)

E_{2n} − E_{n} = (−13.6Z^{2}/(2n)^{2}) – (−13.6Z^{2}/(n)^{2})

= 13.6Z^{2}/n^{2} – 13.6Z^{2}/4n^{2} ……(ii)

On dividing , [E_{4n} − E_{2n}]/ [E_{2n} − E_{n} ] = 1/4