The radius of 2^ nd orbit of He^+of Bohr's model is r_1 and that of fourth orbit of Be^3+ is represented as r_2. Now the ratio r_2r_1 is x :1. The value of x is \_ \_ \_ \_ .

Question

Accepted Answer

Correct answer: 2. (2) The formula to calculate the radius ( r ) of any n^ th Bohr's orbit is given by r=r_0 n^2Z … (i ) where, r_o is Bohr's radius, n is the principal quantum number and Z is the atomic number. Thus, for Helium ion, r_1=r_0 2^22 =2r_0 … . . ( ii ) And, for the Beryllium ion, r_2=r_0 4^24 =4r_0 … . ( iii ) Divide equation (iii) by equation (ii) to obtain the required ratio. r_2r_1= 4r_02r_0 =2 Hence x=2

$The radius of 2^{nd} orbit of He^{+} of Bohr's model is r_{1} and that of fourth orbit of Be^{3 +} is represented as r_{2} . Now the ratio \frac{r _{2}}{r _{1}} is x : 1 . The value of x is____.$

Solution

More Atoms PYQs