Question

Calculate energy of electron which is moving in the orbit that has its radius sixteen times the radius of bohr orbit of h atom

Answer 1

Answer: Energy of electron which is moving in the orbit that has its radius sixteen times the radius of bohr orbit of h atom is-3.4 ev.

Explanation

Radius of Bohr nth orbit : 'a' meter

a=0.529\times 10^{-10}\frac{n^2}{Z}a=0.529×10

−10

Z

n

2

Z = Atomic number

Given: Electron which is moving in the orbit that has its radius sixteen times the radius of Bohr orbit of h atom. (Z=1)

a=0.529\times 10^{-10}\frac{(1)^2}{1}=0.529\times 10^{-10} ma=0.529×10

−10

1

(1)

2

=0.529×10

−10

m

a'= 0.529\times 10^{-10}\frac{n^2}{1}=16a=16(0.529\times 10^{-10}\frac{(1)^2}{1})a

′

=0.529×10

−10

1

n

2

=16a=16(0.529×10

−10

1

(1)

2

)

n=4n=4

Energy of electron which is moving in nth shell:

E(n)=-\frac{1}{n^2}\times 13.6 evE(n)=−

n

2

1

×13.6ev

Energy of electron in 4th orbit of the hydrogen atom:

E(4)=-\frac{1}{(4)^2}\times 13.6 ev=-3.4 evE(4)=−

(4)

2

1

×13.6ev=−3.4ev

Answer 2

Answer:

The energy of the electron is -0.85 eV.

Explanation:

Bohr radius of hydrogen$a_o = 0.0529 nm$

Bohr radius of nth orbit =

$r_n=a_o\times n^2$

$a_o=0.0529 nm$

Given: Radius of nth orbit is 16 times the orbit of hydrogen atom.

$r_n=a_o\times n^2=16\times 0.0529 nm$

$0.0529 nm\times n^2=16\times 0.0529 nm$

n = 4

Energy of nth orbit in hydrogen like atoms is given by:

$E_n=\frac{-13.6 eV\times Z^2}{n^2}$

$E_4=\frac{-13.6 eV\times 1^2}{4^2}=-0.85 eV$

The energy of the electron is -0.85 eV.