NEET Practice Questions (MCQs) with Answers & Solutions

$ \lambda = { 12.27 \over \sqrt v } $ $ = { 12.27 \over \sqrt {64} } = { 12.27 \over 8} =1.553 $ $ \therefore \lambda = 1.534 A ^\circ $

$ K = { p^2 \over 2m } $ $ \therefore p = \sqrt {2Km} $ $ \lambda = h/p = h / \sqrt{2Km} $ $ \therefore \lambda \alpha { 1 \over \sqrt m } $ $ \therefore { \lambda_\alpha \over \lambda_p } = \sqrt{m_p \over m_x} = \sqrt { 1/4} $ $ \therefore { \lambda_\alpha \over \lambda_p } = { 1 \over 2 } $

$ K = vq $ $ { 1 \over 2 } mv^2 = Vq , m^2 v^2 = 2Vqm $ $ \therefore mv = \sqrt { 2Vqm} $ $ \lambda = { h \over mv } = { h \over \sqrt { 2Vqm } } $ $ \therefore \lambda \alpha { 1 \over \sqrt { qm } }$ $ \therefore { \lambda_\alpha \over \lambda_p} = \sqrt { q_p m_p \over q_\alpha m_\alpha } = \sqrt { em_p \over 2e \times 4m_p } = \sqrt { 1 \over 8} $ $ \therefore {\lambda_\alpha \over \lambda_p } = { 1 \over 2 \sqrt 2 } $

Let's match the concepts from Column I with their corresponding properties in Column II:

(A) Planck's theory of quanta: This theory relates to the quantization of oscillator energies, where energy is given by discrete packets called quanta (r).

(B) Einstein's theory of quanta: This theory is related to the photoelectric effect, where light energy is given by hv, indicating that light consists of packets of energy called photons (p).

(C) Bohr's stationary orbit: Bohr's model postulates that electrons revolve in specific orbits with quantized angular momentum (q).

(D) D-Broglie waves: D-Broglie hypothesized that particles like electrons exhibit wave-like properties, which is crucial in the functioning of devices like electron microscopes (s).

So the correct matching is: (A-r) (B-p) (C-q) (D-s).

Let's match the concepts from Column I with their corresponding properties in Column II:

(I) Quantisation of charge: This is demonstrated by Milikan's oil drop experiment, which measured the charge of electrons (S).

(II) Wave nature of light: This is demonstrated by diffraction and interference experiments (P).

(III) Dual nature of matter: This is proposed by the de Broglie hypothesis, which states that particles exhibit both wave and particle properties (Q).

(IV) Particle nature of light: This is explained by the photoelectric effect, where light is shown to have particle-like properties (R).

So the correct matching is: I-S, II-P, III-Q, IV-R.

To solve this matching question, use the following formulas:

1. Energy of photon of wavelength \( \lambda \) is given by \( E = \frac{hc}{\lambda} \). So, I matches with R.
2. The de Broglie wavelength associated with a particle of momentum \( P \) is given by \( \lambda = \frac{h}{p} \). So, II matches with S.
3. Mass of photon in motion is given by \( m = \frac{hf}{c^2} \). So, III matches with Q.
4. The velocity of photon of energy \( E \) and momentum \( P \) is given by \( v = \frac{E}{p} \). So, IV matches with P.

Therefore, the correct matching is: I- R, II- S, III- Q, IV - P.

According to Lenz's law, the direction of the induced current is such that it opposes the change in magnetic flux that caused it. Since the current in the outer loop is increasing clockwise, the magnetic field due to this current is increasing out of the plane. To oppose this increase, the induced current in the inner loop must create a magnetic field into the plane. Hence, the induced current in the inner loop must be counterclockwise.