Show that the ratio of the magnetic dipole moment to the angular momentum
Question: Show that the ratio of the magnetic dipole moment to the angular momentum $\mathrm{I}=\mathrm{mvr}$ is a universal constant for hydrogen like atoms and ions. Find its value. Solution:...
Read More →Calculate the magnetic dipole moment corresponding to the motion
Question: Calculate the magnetic dipole moment corresponding to the motion of the electron in the ground state of a hydrogen atom. Solution:...
Read More →Average lifetime of a hydrogen atom excited to n=2 state is
Question: Average lifetime of a hydrogen atom excited to $n=2$ state is $10^{-8} \mathrm{~s}$. Find the number of revolutions made by the electron on the average before it jumps to the ground state. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in the following:. $f(x)=\frac{2 x}{\log x}$ is increasing in A. $(0,1)$ B. $(1, \mathrm{e})$ C. $(e, \infty)$ D. $(-\infty$, e $)$ Solution:...
Read More →Find the temperature at which the average thermal kinetic energy is equal
Question: Find the temperature at which the average thermal kinetic energy is equal to the energy needed to take a hydrogen atom from its ground state to $\mathrm{n}=3$ state. Hydrogen can now emit red light of wavelength $653.1 \mathrm{~nm}$. Because of Maxwellian distribution of speeds, a hydrogen sample emits red light at temperatures much lower than that obtained from this problem. Assume that hydrogen molecules dissociate into atoms. Solution:...
Read More →The average kinetic energy of molecules in a gas at temperature
Question: The average kinetic energy of molecules in a gas at temperature $t$ is $1.5 \mathrm{kT}$. Find the temperature at which the average kinetic energy of the molecules of hydrogen equals the binding energy of its atoms. Will hydrogen remain in molecular form at this temperature? Take $\mathrm{k}=8.62 \times 10^{-6} \mathrm{eV} / \mathrm{K}$. Solution:...
Read More →According to Maxwell's theory of electrodynamics,
Question: According to Maxwell's theory of electrodynamics, an electron going in a circle should emit radiation of frequency equal to its frequency of revolution. What should be the wavelength of the radiation emitted by a hydrogen atom in ground state if this rule is followed? Solution:...
Read More →Suppose, in certain conditions only those transitions are allowed to hydrogen atoms in
Question: Suppose, in certain conditions only those transitions are allowed to hydrogen atoms in which the principal quantum number $\mathrm{n}$ changes by 2 . Find the smallest wavelength emitted by hydrogen. List the wavelength emitted by hydrogen in the visible range ( $380 \mathrm{~nm}$ to $780 \mathrm{~nm})$. Solution:...
Read More →A spectroscopic instrument can resolve two nearby wavelength
Question: A spectroscopic instrument can resolve two nearby wavelength $\lambda$ and $\lambda+\Delta \lambda$ if $\lambda / \Delta \lambda$ is smaller than 8000 . This is used to study the spectral lines of the Balmer series of hydrogen. Approximately how many lines will be resolved by the instrument? Solution:...
Read More →Find the maximum angular speed of the electron of a hydrogen atom in a stationary orbit.
Question: Find the maximum angular speed of the electron of a hydrogen atom in a stationary orbit. Solution:...
Read More →A gas of hydrogen like ions is prepared in a particular excited state A.
Question: A gas of hydrogen like ions is prepared in a particular excited state A. It emits photons having wavelength equal to the wavelength of the first line of Lyman series together with photons of five other wavelengths. Identify the gas and find the principal quantum number of the state A. Solution:...
Read More →A hot gas emits radiation of wavelengths 46.0 nm,
Question: A hot gas emits radiation of wavelengths $46.0 \mathrm{~nm}, 82.8 \mathrm{~nm}$ and $103.5 \mathrm{~nm}$ only. Assume that the atoms have only two excited states and the difference between consecutive energy levels decreases as energy is increased. Taking the energy of the highest energy state to be zero, find the energies of the ground state and the first excited state. Solution:...
Read More →What is the energy of a hydrogen atom in the first excited state
Question: What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state? Solution:...
Read More →A hydrogen atom in state n=6 makes two successive transitions and reaches the ground state.
Question: A hydrogen atom in state $n=6$ makes two successive transitions and reaches the ground state. In the first transition a photon of $1.13 \mathrm{eV}$ is emitted. Find the energy of the photon emitted in the second transition. What is the value of $\mathrm{n}$ in the intermediate state? Solution:...
Read More →Whenever a photon is emitted by hydrogen in Balmer series,
Question: Whenever a photon is emitted by hydrogen in Balmer series, it is followed by another photon in Lyman series. What wavelength does this latter photon correspond to? Solution:...
Read More →A hydrogen atom in a state having a binding energy of
Question: A hydrogen atom in a state having a binding energy of $0.85 \mathrm{eV}$ makes transition to a state with excitation energy $10.2 \mathrm{eV}$. Identify the quantum numbers $n$ of the upper and the lower energy states involved in the transition. Find the wavelength of the emitted radiation. Solution:...
Read More →Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.
Question: Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom. Solution:...
Read More →A positive ion having just one electron ejects it if a photon of wavelength
Question: A positive ion having just one electron ejects it if a photon of wavelength $228 \mathrm{~A}^{\circ}$ or less is absorbed by it. Identify the ion. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)})$ against the correct answer in the following: $f(x)=\sin x$ is increasing in A. $\left(\frac{\pi}{2}, \pi\right)$ B. $\left(\pi, \frac{3 \pi}{2}\right)$ C. $(0, \pi)$ D. $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ Solution:...
Read More →A group of hydrogen atoms are prepared in n=4 states.
Question: A group of hydrogen atoms are prepared in $n=4$ states. List the wavelength that are emitted as the atoms make transition and return to $\mathrm{n}=2$ states. Solution:...
Read More →Find the first excitation potential of He+ion.
Question: Find the first excitation potential of $\mathrm{He}^{+}$ion. Find the ionization potential of $\mathrm{Li}^{++}$ion. Solution:...
Read More →A hydrogen atom emits ultraviolet radiation of wavelength
Question: A hydrogen atom emits ultraviolet radiation of wavelength $102.5 \mathrm{~nm}$. What are the quantum numbers of the states involved in the transition? Solution:...
Read More →Find the radius and energy of a He+ ion in the state n=2.
Question: Find the radius and energy of $\mathrm{He}^{+}$ion in the state $\mathrm{n}=2$. Solution:...
Read More →Find the binding energy of a hydrogen atom in the state n=2.
Question: Find the binding energy of a hydrogen atom in the state $n=2$. Solution:...
Read More →Evaluate Rydberg constant by putting the values of the fundamental
Question: Evaluate Rydberg constant by putting the values of the fundamental constants in its expression. Solution:...
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