An electron in a hydrogen atom makes a transition n? ? n?, where n? and n? are the principal quantum numbers of the two states. Assume Bohr model to be valid.

Question

An electron in a hydrogen atom makes a transition $n_{1} \to n_{2}$ , where $n_{1}$ and $n_{2}$ are the principal quantum numbers of the two states. Assume Bohr model to be valid.

	Column-I		Column-II
A)	The electron emits an energy of 2.55 eV	p)	$n_{1} = 2, n_{2} = 1$
B)	Time period of the electron in the initial state is eight times that in the final state	q)	$n_{1} = 4, n_{2} = 2$
C)	Speed of electron become two times	r)	$n_{1} = 5, n_{2} = 3$
D)	Radius of orbit of electron becomes 4.77 $A^{0}$	s)	$n_{1} = 6, n_{2} = 3$
		t)	$n_{1} = 8, n_{2} = 4$

Smart Achievers · Accepted Answer

(3)

$E_{n} = - 13.6 \frac{Z^{2}}{n^{2}} e V, r_{n} = 0.529 \frac{n^{2}}{Z} Å, V_{n} = 2.2 \times 10^{6} \frac{Z}{n} m / s, T = \frac{2 π r_{n}}{v_{n}} .$

Solution

1 A→p, B→p,t, C→p,q,t, D→r

2 A→p, B→p,t, C→p,q,s,t, D→r

3 A→q, B→p,q,s,t, C→p,q,s,t, D→r,s

4 A→r, B→p, C→p,q,s,t, D→q

Ans.
(3)

$E_{n} = - 13.6 \frac{Z^{2}}{n^{2}} e V, r_{n} = 0.529 \frac{n^{2}}{Z} Å, V_{n} = 2.2 \times 10^{6} \frac{Z}{n} m / s, T = \frac{2 π r_{n}}{v_{n}} .$

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