NEET Practice Questions (MCQs) with Answers & Solutions

The probability of finding a particle at a given point in space is directly proportional to the square of the wave function's magnitude, $| \\Psi|^2$. This is because the probability density is given by $\\rho(x,y,z) = | \\Psi(x,y,z)|^2$. Therefore, the correct option is 'directly proportional to $ | \\Psi \\Psi ^ * | $'.

$ E = hf = h { C \over \lambda } $ $ = { 6.62 \times 10^ {-34} \times 3.0 \times 10^8 } $ $ = 3.31 \times 10^ {-19 } J $ $ = { 3.31 \times 10^{-19 } \over 1.6 \times 10 ^ {-19 }} eV $ $ = 2.06 eV $

$ hf_0 = \phi $ $ \therefore f_0 = { \phi \over h } = { 5.3 \times 10^{-19} \times 1.6 \over 6.62 \times 10^ {-34} } Hz $ $ = 1.3 \times 10^{15 } Hz $

$ eV_0 = { 1 \over 2 } mv^2 max = 3.8 eV $ $ \therefore V_0 = 3.8 V $ $ {1 \over 2 } mv^2 max = eV_0 = hf - \phi = hf - hf_0 = h ({c \over \lambda} - {c \over \lambda_0} ) $

When the frequency of the incident radiation is increased, while keeping the intensity constant, the energy of each photon increases according to the relation $E = h\nu$ (where $\nu$ is the frequency and $h$ is Planck's constant). Therefore, the energy of the emitted photoelectrons will increase.

In the context of electromagnetic radiation in a cavity, the energy of an oscillator being equal to $5hf$ indicates that the oscillator has energy levels that can be occupied by photons. Since the energy is an integer multiple of $hf$, it suggests that the oscillator has a one-to-one correspondence with the photons. Thus, the oscillator is equivalent to 1:1.

In metals, valence electrons can move freely within the metal but they are not completely free. They move according to their wave functions inside the metal. This is due to the quantum mechanical nature of electrons which describes their behavior in terms of wave functions.