(a) Using the Bohr’smodel calculate the speed of the electron in a hydrogen atom in the n= 1, 2, and 3 levels. (b) Calculate the orbital period in each ofthese levels.
(a) Using the Bohr’smodel calculate the speed of the electron in a hydrogen atom in the n= 1, 2, and 3 levels. (b) Calculate the orbital period in each ofthese levels.
(a) Let ν1 be the orbital speed of theelectron in a hydrogen atom in the ground state level, n1= 1. For charge (e) of an electron, ν1 isgiven by the relation,
Where,
e= 1.6 × 10−19 C
∈0= Permittivity of free space = 8.85 × 10−12N−1 C2 m−2
h= Planck’s constant = 6.62 × 10−34 Js
Forlevel n2 = 2, we can write the relation for thecorresponding orbital speed as:
And,for n3 = 3, we can write the relation for thecorresponding orbital speed as:
Hence,the speed of the electron in a hydrogen atom in n = 1, n=2,and n=3 is 2.18 × 106 m/s, 1.09 × 106m/s, 7.27 × 105 m/s respectively.
(b) Let T1be the orbital period of the electron when it is in level n1= 1.
Orbitalperiod is related to orbital speed as:
Where,
r1= Radius of the orbit
h= Planck’s constant = 6.62 × 10−34 Js
e= Charge on an electron = 1.6 × 10−19 C
∈0= Permittivity of free space = 8.85 × 10−12N−1 C2 m−2
m= Mass of an electron = 9.1 × 10−31 kg
Forlevel n2 = 2, we can write the period as:
Where,
r2= Radius of the electron in n2 = 2
And,for level n3 = 3, we can write the period as:
Where,
r3= Radius of the electron in n3 = 3
Hence,the orbital period in each of these levels is 1.52 × 10−16s, 1.22 × 10−15 s, and 4.12 × 10−15s respectively.
(a) Let ν1 be the orbital speed of theelectron in a hydrogen atom in the ground state level, n1= 1. For charge (e) of an electron, ν1 isgiven by the relation,
Where,
e= 1.6 × 10−19 C
∈0= Permittivity of free space = 8.85 × 10−12N−1 C2 m−2
h= Planck’s constant = 6.62 × 10−34 Js
Forlevel n2 = 2, we can write the relation for thecorresponding orbital speed as:
And,for n3 = 3, we can write the relation for thecorresponding orbital speed as:
Hence,the speed of the electron in a hydrogen atom in n = 1, n=2,and n=3 is 2.18 × 106 m/s, 1.09 × 106m/s, 7.27 × 105 m/s respectively.
(b) Let T1be the orbital period of the electron when it is in level n1= 1.
Orbitalperiod is related to orbital speed as:
Where,
r1= Radius of the orbit
h= Planck’s constant = 6.62 × 10−34 Js
e= Charge on an electron = 1.6 × 10−19 C
∈0= Permittivity of free space = 8.85 × 10−12N−1 C2 m−2
m= Mass of an electron = 9.1 × 10−31 kg
Forlevel n2 = 2, we can write the period as:
Where,
r2= Radius of the electron in n2 = 2
And,for level n3 = 3, we can write the period as:
Where,
r3= Radius of the electron in n3 = 3
Hence,the orbital period in each of these levels is 1.52 × 10−16s, 1.22 × 10−15 s, and 4.12 × 10−15s respectively.
