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Test: Bohr’s Model of Atom


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10 Questions MCQ Test Physics Class 12 | Test: Bohr’s Model of Atom

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Test: Bohr’s Model of Atom - Question 1

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

Detailed Solution for Test: Bohr’s Model of Atom - Question 1

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

Test: Bohr’s Model of Atom - Question 2

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

Detailed Solution for Test: Bohr’s Model of Atom - Question 2

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
 

Test: Bohr’s Model of Atom - Question 3

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

Detailed Solution for Test: Bohr’s Model of Atom - Question 3

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

Test: Bohr’s Model of Atom - Question 4

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

Detailed Solution for Test: Bohr’s Model of Atom - Question 4

The angular momentum L =me​vr is on integer multiple of h​/2π
mvr= nh​/2π
For, n=1
mvr= h​/2π
The correct answer is option B.

Test: Bohr’s Model of Atom - Question 5

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

Detailed Solution for Test: Bohr’s Model of Atom - Question 5

r=(0.529Å)n2/7
r ∝n2

*Multiple options can be correct
Test: Bohr’s Model of Atom - Question 6

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
iv. the magnitude of potential energy of the electron in any orbit is greater than its kinetic energy​

Detailed Solution for Test: Bohr’s Model of Atom - Question 6

Statement i. Radius of Bohr's orbit of hydrogen atom is given by
r= n2h2​/4π2mKze2
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/2π – 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 wrong.
Statement iv.
According to Bohr's theory
Angular momentum of electron in an orbit will be Integral multiple of (h/2π)
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.

Test: Bohr’s Model of Atom - Question 7

To explain his theory Bohr used:

Detailed Solution for Test: Bohr’s Model of Atom - Question 7

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

Test: Bohr’s Model of Atom - Question 8

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

Test: Bohr’s Model of Atom - Question 9

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

Detailed Solution for Test: Bohr’s Model of Atom - Question 9

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

Test: Bohr’s Model of Atom - Question 10

The ratio of volume of atom to volume of nucleus is​

Detailed Solution for Test: Bohr’s Model of Atom - Question 10

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

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