Question

In hydrogen atom, an electron jumps from
bigger orbit to smaller orbit so that radius
of smaller orbit is one-fourth of radius of
bigger orbit. If speed of electron is bigger
orbit was v, the speed in smaller orbit is
V
A
2.
V
2v​

Answer 1

Answer:

Radius of nth orbit,

r

n

∝

n

2

rn∝n2

 

r

n big

r

n small

=

n

2

big

n

2

small

=

4

1

rn bigrn small=n2bign2small=41

(given)  

Rightarrow

n

big

n

small

=2

nbignsmall=2

 

Rightarrow

n

small

n

big

=

1

2

nsmallnbig=12

 

Velocity of electron in nth orbit  

v

n

∝

1

n

vn∝1n

v

(n big)

v

(n small)

=

n

small

n

big

=

1

2

v(n big)v(n small)=nsmallnbig=12

Rightarrow

V

n small

=2(

v

n big

)=2v

Explanation: