Question

If in bohr's model, for uni electronic atom, time period of revolution is represented as tn,z where n represents shell no. And z represents atomic number then the value of t1,2 : t2,1 will be :- (1) 8 : 1 (2) 1 : 8 (3) 1: 1 (4) 1 : 32

Answer 1

If in bohr's model, for uni electronic atom, time period of revolution is represented as tn,z where n represents shell no. And z represents atomic number then the value of t1,2 : t2,1 will be :- (1) 8 : 1 (2) 1 : 8 (3) 1: 1 (4) 1 : 32...

answer : option (4) 1 : 32

according to Bohr's model of atom,

• radius of nth orbit , $r_n\propto\frac{n^2}{Z}$
• velocity of electron in nth orbit, $v_n\propto\frac{Z}{n}$

we know, time period of electron in nth orbit is given by, $T_n=\frac{2\pi r_n}{v_n}$

hence, $T_n\propto\frac{\frac{n^2}{Z}}{\frac{Z}{n}}$

⇒ $T_n\propto\frac{n^3}{Z^2}$

so, $\frac{T_{(1,2)}}{T_{(2,1)}}=\frac{\frac{(1)^3}{(2)^2}}{\frac{(2)^3}{(1)^2}}$

= (1/4)/(8/1) = 1/32

hence, option (4) is correct choice.

Answer 2

Explanation:

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