Question

Calculate the ratio of the radius of 1st orbit of H atom to that of 4th orbit

Answer 1

Answer:

$\large \text{ \dfrac{r_{1}}{r_2} =\dfrac{1}{16} }$

Explanation:

We have formula for calculating radius given by Bohr.

$\large \text{Radius of orbit ( r ) =\dfrac{n^2.h^2}{4 \pi. m.Ze^2} }$

Where n = principal quantum number ( orbit number ) .

h = planck constant

Z e = charge on nucleus.

m = mass of the electron.

Now finding ratio and putting n = 1 & n = 4

$\large \text{ \dfrac{r_{1}}{r_2} =\dfrac{\dfrac{1^2.h^2}{4 \pi. m.Ze^2}}{\dfrac{4^2.h^2}{4 \pi. m.Ze^2}} }\\\\\\\large \text{ \dfrac{r_{1}}{r_2} =\dfrac{\dfrac{1^2.\cancel{h^2}}{\cancel4 \pi. m.Ze^2}}{\dfrac{4^2.\cancel h^2}{\cancel4 \pi. m.Ze^2}} }\\\\\\\large \text{ \dfrac{r_{1}}{r_2} =\dfrac{1}{16} }$

Thus we get answer.

Some more important thing to know :

To find angular momentum and wave length given by Bohr and de Broglie respectively.

$\large 1. \ mvr=\dfrac{nh}{2\pi} \\\\\\\large 2. \ \lambda=\dfrac{h}{mv}$

Answer 2

Answer:

Explanation:

Its 10.2 eV or 2.55 eV.

R= .529 *(n^2/Z )

n = no. Of orbit

Z =atomic no.

Given R1/R2 = 4:1

n1 ^2/n2^ 2 = 4:1

n1/n2 = 2:1

Among 1st 4 orbits

n1 = 4 or 2

n2 =2 or 1

If n1 = 4 then n2 =2

Or n1= 2 then n2 = 1

Use energy equation then

E = -13.6 *(Z^2 / n^2 )

For case 1 ∆E = 2.55 eV

For case 2 ∆E = 10.2 ev