In hydrogen and hydrogen-like atoms, the ratio of E4n- E2n and E2n- En varies with atomic number z and principal quantum number n as

Q. In hydrogen and hydrogen-like atoms, the ratio of E4n– E2n and E2n– En varies with atomic number z and principal quantum number n as

(a)    Z2/n2

(b)  Z4/n4

(c)    Z/n

(d) None of these

Ans: (d)

Sol: E4n − E2n = (−13.6Z2/(4n)2) – (−13.6Z2/(2n)2)

= 13.6Z2/4n2 – 13.6Z2/16n2         ……..(i)

E2n − En = (−13.6Z2/(2n)2) – (−13.6Z2/(n)2)

= 13.6Z2/n2 – 13.6Z2/4n2             ……(ii)

On dividing , [E4n − E2n]/ [E2n − En ] = 1/4

 

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