Atoms, Nuclei & Radioactivity Test

Result

Atoms, Nuclei & Radioactivity Test - 2

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0.25

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/n² ₁ −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 / -0.25

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 /2nh ϵ₀
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 ×10⁸ ms⁻¹
The speed of light is 3 ×10⁸
Hence,
v/c =0.0219 ×10⁸ /3 ×10⁸
v/c =1/137
Question 3
1 / -0.25

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.=(1/4 πε) x (e² /2r)
Question 4
1 / -0.25

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

A
2h

B
h/2 π

C
2 π/h

D
h/π

Solution

The angular momentum L =m_e vr is on integer multiple of h /2 π
mvr= nh /2 π
For, n=1
mvr= h /2 π
The correct answer is option B.
Question 5
1 / -0.25

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=(0.529 Å)n² /7
r ∝n²
Question 6
1 / -0.25

Select an incorrect alternative:
i. the radius of the nth orbit is proprtional to n2
ii. the total energy of the electron in the nth orbit is inversely proportional to n
iii. the angular momentum of the electron in nth orbit is an integral multiple of h/2 π
iv. the magnitude of potential energy of the electron in any orbit is greater than its kinetic energy

A
Statement i

B
Statement iv

C
Statement ii

D
Statement iii
Solution
Statement i. Radius of Bohr 's orbit of hydrogen atom is given by
r= n2h2 /4 π2mKze2
or, r=(0.59A ˚)(n2 /z)
So, from expression we found r ∝n2
Hence the 1st statement is correct.
Statement ii.
We know that
En=-13.6 x z2/n2
So, En ∝1/n2
Hence the 2nd statement is wrong.
Statement iii. Bohr defined these stable orbits in his second postulate. According to this postulate:
An electron revolves around the nucleus in orbits
The angular momentum of revolution is an integral multiple of h/2 π–where Planck ’s constant [h = 6.6 x 10-34 J-s].
Hence, the angular momentum (L) of the orbiting electron is: L = nh/2 π
Hence the 3rd statement is correct.
Statement iv. According to Bohr 's theory
Angular momentum of electron in an orbit will be Integral multiple of (h/2 π)
Magnitude of potential energy is twice of kinetic energy of electron in an orbit
∣P.E ∣=2 ∣K.E ∣
K.E=(13.6ev)( z2/n2)
Hence, The 4th statement is correct.
Question 7
1 / -0.25

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 I ω=nh2 π
where n=1,2,3,...etc
Question 8
1 / -0.25

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 9
1 / -0.25

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/2 π(for first orbit)
⇒m ωr² =h2 π⇒m ×2 πv ×r² =h/2 π
⇒v=h/4 π² mr²
Question 10
1 / -0.25

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