Atoms and Nuclei

Question 1

A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the nth orbit and the particle's speed v in the orbit depend on n as

Accepted Answer

r ∝ n^(2/3) and v ∝ n^(1/3). The constant force supplies the centripetal force, so mv²/r = F fixes r proportional to v². Bohr quantisation mvr = nh/2π then gives v x v² proportional to n, so v ∝ n^(1/3) and r ∝ n^(2/3).

Answer

r ∝ n^(1/3) and v ∝ n^(1/3)

Answer

r ∝ n^(1/3) and v ∝ n^(2/3)

Answer

r ∝ n^(4/3) and v ∝ n^(−1/3)

Question 2

Consider the following nuclear reaction: ²³⁸U → ²³⁴Th + ⁴He. Take masses of ²³⁸U, ²³⁴Th and ⁴He as 238.050 u, 234.043 u and 4.003 u, respectively. The Q value for the reaction, in keV, is: [Given: 1 u = 931.5 MeV c⁻²]

Accepted Answer

3726. The Q value is the mass defect converted to energy. Δm = 238.050 − (234.043 + 4.003) = 0.004 u, and at 931.5 MeV per atomic mass unit that is 0.004 × 931.5 = 3.726 MeV, or 3726 keV.

Answer

3730

Answer

3736

Answer

3740

Question 3

Given below are two statements. In the light of the above statements, choose the correct answer from the options given below. Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their characteristic spectrum.

Accepted Answer

Statement I is correct but Statement II is incorrect. Statement I is correct — an atom holds as many electrons as protons, so the charges balance exactly. Statement II is incorrect as a general claim: an atom in its ground state emits nothing, and a characteristic spectrum appears only when atoms are excited and then de-excite. Classical physics in fact predicted that atoms should be unstable, which is what Bohr’s postulates were introduced to fix.

Answer

Both Statement I and Statement II are incorrect

Answer

Statement I is incorrect but Statement II is correct

Answer

Both Statement I and Statement II are correct

Q1.A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the nth orbit and the particle's speed v in the orbit depend on n as

Q2.Consider the following nuclear reaction: ²³⁸U → ²³⁴Th + ⁴He. Take masses of ²³⁸U, ²³⁴Th and ⁴He as 238.050 u, 234.043 u and 4.003 u, respectively. The Q value for the reaction, in keV, is: [Given: 1 u = 931.5 MeV c⁻²]

Q3.Given below are two statements. In the light of the above statements, choose the correct answer from the options given below.