Given below are two statements:
Statement-I: The de Broglie wavelength (\(\lambda\)) associated with a moving particle is related to its momentum (\(p\)) as \(\lambda = \frac{h}{p}\).
Statement-II: Photons are electrically neutral and are not deflected by electric and magnetic fields.
In the light of above statements choose the most appropriate answer from the options given below.
1. Statement-I is correct but statement-II is incorrect
2. Statement-I is incorrect but statement-II is correct
3. Both statements-I and II are correct
4. Both statements-I and II are incorrect
View Answer
Statement-I is the basic de Broglie relationship \(\lambda = h/p\) which is correct. Statement-II is also correct as photons carry no charge and do not interact with electromagnetic fields.
In a hypothetical situation, all the atoms in a hydrogen sample are excited to same state. During de-excitation, photon with lowest energy was found to have \(0.66\text{ eV}\). The photon with the highest energy will have energy equal to
1. \(12.1\text{ eV}\)
2. \(10.8\text{ eV}\)
3. \(12.75\text{ eV}\)
4. \(13.6\text{ eV}\)
View Answer
For hydrogen atom, \(E_n - E_{n-1} = 0.66\text{ eV}\) corresponds to \(n = 5\) to \(n = 4\) transition (since \(E_5 - E_4 = -0.85 - (-1.51) = 0.66\text{ eV}\)). The highest energy photon is emitted for transition from \(n = 5\) to \(n = 1\), which is \(E_5 - E_1 = -0.85 - (-13.6) = 12.75\text{ eV}\).
Consider the following statements:
a. The density of the nuclear matter is independent of the size of the nucleus.
b. Fusion of light nuclei to form heavier nuclei is possible at room temperature.
c. Electron and positron are particle-antiparticle pair.
The correct statement(s) is/are
1. Both a and c
2. Both a and b
3. Both b and c
4. Only b
View Answer
Nuclear density is constant for all nuclei, hence independent of size (Statement a is true). Nuclear fusion requires extremely high temperatures (Statement b is false). Positron is the antiparticle of electron (Statement c is true).
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Binding energy per nucleon for atoms having mass number between \(30\) to \(170\), almost remains same.
Reason (R): Nuclear force is a short range force and hence get saturated.
In the light of the above statements, choose the correct answer from the options given below.
1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The binding energy per nucleon is nearly constant in the range \(30 < A < 170\) due to the short-range nature and saturation property of nuclear forces. Thus, both Assertion and Reason are true and the Reason is the correct explanation.
The correct statement regarding nuclear force is
1. It is short range and charge dependent.
2. It is long range and charge dependent.
3. It is short range and charge independent.
4. It is long range and charge independent.
View Answer
Nuclear forces are very short-range forces (acting within femtometers) and they are charge independent, meaning the force between proton-proton, neutron-neutron, and proton-neutron is approximately the same.
In a photoelectric effect, a metal having threshold frequency ( f_0 ) is used. When it is irradiated with photons of frequency ( 2f_0 ), the stopping potential comes out to be ( V_0 ). If the same metal is irradiated with photons of frequency ( 3f_0 ), then the stopping potential will be equal to
1. \( 2V_0 \)
2. \( \frac{2}{3}V_0 \)
3. \( \frac{3}{2}V_0 \)
4. \( V_0 \)
View Answer
From Einstein's photoelectric equation, \( eV_0 = h(2f_0) - hf_0 = hf_0 \). For frequency ( 3f_0 ), \( eV' = h(3f_0) - hf_0 = 2hf_0 = 2(eV_0) \), which gives \( V' = 2V_0 \).