Question

which of the following orbits of hydrogen atom should have the values of their radii in the ratio of 1:4

Answer 1

Answer:                                                                                                                                      

Both option a and b are correct                                                                                                              

A option is K and L,B option is L and N

Answer 2

K,L and L,N orbits of hydrogen atom should have the values of their radii in the ratio of 1:4

Given

orbits of hydrogen atom  have  radii in the ratio of 1:4.

To find

We need to find the orbit with radii in ratio 1:4

Solution

Radii of Bohr's orbit = 0.529 × $\frac{n^{2} }{z}$

For Hydrogen atom z = 1

so radii becomes,

                    r = 0.529 × $n^{2}$

Here the radius ratio is 1 : 4

as r α  $n^{2}$

$\frac{r_{1} }{r_{2} }$ = $\frac{n^{2} _{1} }{n^{2} _{2} }$

$\frac{1}{4}$  =  $\frac{n^{2} _{1} }{n^{2} _{2} }$

$n^{2} _{2}$  = 4 $n^{2} _{1}$

$\frac{n_{2} }{n_{1} }$ = 2

For K shell , n = 1

      L shell , n = 2

       M shell , n =3

       N shell , n = 4

so

  K = 1 and L = 2                ⇒ ratio = 2

  L = 2  and N = 2            ⇒ ratio = 2

K,L and L,N orbits of hydrogen atom should have the values of their radii in the ratio of 1:4

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