Hydrogen Spectra

In a laboratory experiment on emission from atomic hydrogen in a discharge tube, only a few lines are observed whereas many lines are present in the hydrogen spectrum of a star. This is because in a laboratory,

In which of the following systems will the wavelength corresponding to $n=2$ to $n=1$ be minimum?

Suppose in certain condition only those transitions are allowed to hydrogen atoms in which the principal quantum number $n$ changes by $2$. (a) Find the smallest wavelength emitted by hydrogen. (b) List the wavelength emitted by hydrogen in the visible range $(380 \mathrm{nm} \mathrm{to} 780 \mathrm{nm})$.

A spectroscopic instrument can resolve two nearby wavelengths $\lambda$ and $\lambda +∆\lambda$, if $\frac{\lambda }{∆\lambda }$ 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?

Whenever a photon is emitted by hydrogen in the Balmer series, it is followed by another photon in the Lyman series. What wavelength does this latter photon corresponds to?

A positive ion having just one electron ejects it if a photon of wavelength $228 \stackrel{\circ }{\mathrm{A}}$ or less is absorbed by it. Identify the ion.

An atom is in its excited state. Does the probability of it coming to the ground state depend on whether the radiation is already present or not? If yes, does it depend on the wavelength of the radiation present?

We have stimulated emission and spontaneous emission. Do we also have stimulated absorption and spontaneous absorption?

The difference in the frequencies of series limit of Lyman and Balmer series is equal to the frequency of the first line of the Lyman series. Explain.

Balmer series was observed and analysed before the other series. Can you suggest a reason for such an order?

When white radiation is passed through a sample of hydrogen gas at room temperature, absorption lines are observed in Lyman series only. Explain.

Which all wavelengths will be emitted by a sample of atomic Hydrogen gas (in ground state) if electrons of energy $12.2 \mathrm{eV}$ collide with atoms of the gas?

How many wavelengths are emitted by atomic hydrogen in visible range $(380 \mathrm{nm}-780 \mathrm{nm})$ in the range $50 \mathrm{nm}$ to $100 \mathrm{nm}$?

Consider an excited hydrogen atom in the state $n$ moving with a velocity $\upsilon \left(\upsilon <<c\right)$. It emits a photon in the direction of its motion and changes its state to a lower state $m$. Apply momentum and energy conservation principles to calculate the frequency $v$ of the emitted radiation. Compare this with the frequency $v_0$ emitted, if the atom were at rest.

A filter transmits only the radiation of wavelength greater than $440 \mathrm{nm}$. The radiation from a hydrogen discharge tube goes through such a filter and is incident on a metal of work function $2.0 \mathrm{eV}$. Find the stopping potential which can stop the photoelectrons.

Radiation from hydrogen discharge tube falls on a cesium plate. Find the maximum possible kinetic energy of the photoelectrons. Work function of cesium is $1.9 \mathrm{eV}$.

Light from Balmer series of hydrogen is able to eject photoelectrons from a metal. What can be the maximum work function of the metal?

The light emitted in the transition $n=3$ to $n=2$ in hydrogen is called ${\mathrm{H}}_{\mathrm{\alpha }}$ light. Find the maximum work function a metal can have so that ${\mathrm{H}}_{\mathrm{\alpha }}$ light can emit photoelectrons from it.

When a photon is emitted from an atom, the atom recoils. The kinetic energy of recoil and the energy of the photon come from the difference in energies between the states involved in the transition. Suppose a hydrogen atom changes its state from $n=3$ to $n=2$. Calculate the fractional change in the wavelength of light emitted due to the recoil.

When a photon is emitted by a hydrogen atom, the photon carries momentum with it. (a) Calculate the momentum carried by the photon when a hydrogen atom emits light of wavelength $656.3 \mathrm{nm}$. (b) With what speed does the atom recoil during this transition? (c) Find the kinetic energy of the recoil of the atom.