Atomic Test

Result

Atomic Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

If the electron in H atom jumps from the third orbit to second orbit, the wavelength of the emitted radiation is given by

A

B

C

D

Solution

We know that
1/λ=R(1/n²₁−1/n²₂)
1/λ=R(1/2²) − (1/3²)⇒R(1/4)−(1/9)
1/λ=(9−4/36)R=5R/36⇒λ=36/5R
Question 2
1 / -0

The ratio of the speed of the electron in the ground state of hydrogen atom to the speed of light is

A
1/237

B
2/137

C
1/137

D
1/2

Solution

The speed of revolving electron in nth state of hydrogen atom is:
v=e²/2nhϵ₀
For n=1,
v= (1.6×10⁻¹⁹)²/2(1)(6.6×10⁻³⁴)(8.85×10⁻¹²)
v=2.56×10⁻³⁸/116.82×10⁻⁴⁶

v=0.0219×10⁸ms⁻¹
The speed of light is 3×10⁸
Hence,
v/c=0.0219×10⁸/3×10⁸
v/c=1/137
Question 3
1 / -0

In hydrogen atom the kinetic energy of electron in an orbit of radius r is given by

A

B

C

D

Solution

K.E. of nth orbit
=> (1/k) Ze²/2r
For H atom,
K.E.=(1/4πε) x (e²/2r)
Question 4
1 / -0

In hydrogen atom the angular momentum of the electron in the lowest energy state is

A
2h

B
h/2π

C
2π/h

D
h/π

Solution

The angular momentum L =m_evr is on integer multiple of h/2π
mvr= nh/2π
For, n=1
mvr= h/2π
The correct answer is option B.
Question 5
1 / -0

According to Bohr model of hydrogen atom, the radius of stationary orbit characterized by the principal quantum number n is proportional to

A
1/n

B
n

C
1/n²

D
n²

Solution

r=(0.529Å)n²/7
r ∝n²
Question 6
1 / -0

To explain his theory Bohr used:

A
conservation of quantum frequency

B
conservation of energy

C
conservation of linear momentum

D
conservation of angular momentum

Solution

Bohr used conservation of angular momentum.
For stationary orbits, Angular momentum Iω=nh2π
where n=1,2,3,...etc
Question 7
1 / -0

In Bohr model of hydrogen atom, radiation is emitted when the electron

A
jumps from higher orbit into the lower orbit

B
the electron escapes from the orbit

C
jumps from lower orbit into the higher orbit

D
revolves in an orbit
Question 8
1 / -0

The number of times an electron goes around the first Bohr orbit in a second is

A

B

C

D

Solution

We know that,
mvr=h/2π (for first orbit)
⇒mωr²=h2π⇒m×2πv×r²=h/2π
⇒v=h/4π²mr²
Question 9
1 / -0

The ratio of volume of atom to volume of nucleus is

A
1/1000

B
10

C
10¹⁵

D
10¹⁰

Solution

The ratio of the volume of the atom and the volume of the nucleus is 10¹⁵
The radius of an atomic nucleus is of the order of 10⁻¹³cm or 10⁻¹⁵m or one Fermi unit.
On the other hand, the radius of an atom is of the order of 10⁻⁸cm or 10⁻¹⁰m or one angstrom unit.
Note:
The radius of nucleus is much smaller than atomic radius.
The ratio of atomic radius to radius of nucleus is 10⁻¹⁰m /10⁻¹⁵m =10⁵
Volume is proportional to cube of radius.
The ratio of atomic radius to radius of nucleus is (10⁵)³=10¹⁵