The ratio between Bohr radii are

Question

The ratio between Bohr radii are (A) 1: 2: 3 (B) 2: 4: 6 (C) 1: 4: 9 (D) 1: 3: 5

Tardigrade Admin · Accepted Answer

For hydrogen and H-like atom Bohrs radius of orbit rn=(n2h2/4π 2kZme2)=(n2h2ε 0/π mZe2)=0.53(n2/Z) overset texto mathop textA ⇒ rn=(n2/Z) ∴ Ratio between Bohr radii =1:4:9:... where n=1,2,3...

Q. The ratio between Bohr radii are

1 : 2 : 3

2 : 4 : 6

1 : 4 : 9

1 : 3 : 5

For hydrogen and H-like atom Bohrs radius of orbit $r_{n} = \frac{n ^{2} h ^{2}}{4 π ^{2} k Z m e ^{2}} = \frac{n ^{2} h ^{2} ε _{0}}{πm Z e ^{2}} = 0.53 \frac{n ^{2}}{Z} A o$ $\Rightarrow$ $r_{n} = \frac{n ^{2}}{Z}$ $∴$ Ratio between Bohr radii $= 1 : 4 : 9 : ...$ where $n = 1, 2, 3...$

Q. The ratio between Bohr radii are

1 : 2 : 3

2 : 4 : 6

1 : 4 : 9

1 : 3 : 5

For hydrogen and H-like atom Bohrs radius of orbit rn​=4π2kZme2n2h2​=πmZe2n2h2ε0​​=0.53Zn2​Ao ⇒ rn​=Zn2​ ∴ Ratio between Bohr radii =1:4:9:... where n=1,2,3...

For hydrogen and H-like atom Bohrs radius of orbit $r_{n} = \frac{n ^{2} h ^{2}}{4 π ^{2} k Z m e ^{2}} = \frac{n ^{2} h ^{2} ε _{0}}{πm Z e ^{2}} = 0.53 \frac{n ^{2}}{Z} A o$ $\Rightarrow$ $r_{n} = \frac{n ^{2}}{Z}$ $∴$ Ratio between Bohr radii $= 1 : 4 : 9 : ...$ where $n = 1, 2, 3...$