Question

Practice entering numbers that include a power of 10 by entering the diameter of a hydrogen atom in its ground state, dH=1.06×10−10m, into the answer box.

Express the diameter of a ground-state hydrogen atom in meters using a power of 10. Do not enter the units; they are provided to the right of the answer box.

dh=

Answer 1

Step-by-step explanation:

According to Bohr's model, angular momentum is given by :

`L=(nh)/(2\pi)`

Since, L = m v r

So,
`mvr=(nh)/(2\pi)`

`v=(nh)/(2\pi mr)`...................(1)

The electrostatic force is balanced by the electrostatic force as :

`(ke^2)/(r^2)=(mv^2)/(r)`

From equation (1),

`r=(n^2h^2)/(4\pi^2mke^2)`

Where

r is the radius of ground state hydrogen atom

n is the orbit

h is Planck's constant

m is the mass of electron

k is the electrostatic constant

`r=(1^2(6.62* 10^(-34))^2)/(4\pi^2* 9.1* 10^(-31)* 9* 10^9* (1.6* 10^(-19))^2)`

`r=5.29* 10^(-11)\ m`

Diameter of hydrogen atom,

`D=2r=2* 5.29* 10^(-11)`

`D=1.058* 10^(-10)\ m`

So, the diameter of a ground-state hydrogen atom is
`1.058* 10^(-10)\ m`. Hence, this is the required solution.