Question

The ratio of the radius of 1st orbit of h atom to that of its 4th excited state is

Answer 1

The radii are in the ratio

6

:

3

:

2

.

Explanation:

The radii of the first orbits of a hydrogen-like ion are given by the equation

r

=

ħ

2

Z

m

e

k

e

e

2

Since everything except

Z

is constant, we can rewrite the formula as

r

=

k

Z

Then the ratios of the three radii for

Z

=

1

,

2

and

3

are

r

1

:

r

2

:

r

3

=

1

1

:

1

2

:

1

3

=

6

:

3

:

2

Hope it helps...