(R = Rydberg constant)
Hydrogen Balmer Series Identification
The wave number ($\bar{\nu}$) of spectral lines in a hydrogen atom is calculated using the Rydberg formula:
$ \bar{\nu} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) $
where $R$ is the Rydberg constant, $n_f$ is the final principal quantum number, and $n_i$ is the initial principal quantum number ($n_i > n_f$). The Balmer series specifically corresponds to transitions where the electron falls to the second energy level, meaning $n_f = 2$.
Balmer Series Wave Number Calculations
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Step 1: Calculate for $n_i=3$. For the transition $n_i=3 \to n_f=2$:
$ \bar{\nu} = R \left( \frac{1}{2^2} - \frac{1}{3^2} \right) = R \left( \frac{1}{4} - \frac{1}{9} \right) = R \left( \frac{9-4}{36} \right) = \frac{5R}{36} $ -
Step 2: Calculate for $n_i=4$. For the transition $n_i=4 \to n_f=2$:
$ \bar{\nu} = R \left( \frac{1}{2^2} - \frac{1}{4^2} \right) = R \left( \frac{1}{4} - \frac{1}{16} \right) = R \left( \frac{16-4}{64} \right) = R \left( \frac{12}{64} \right) = \frac{3R}{16} $ - Step 3: The question asks to identify the set of spectral lines belonging to the Balmer series. We have calculated two known Balmer lines: $ \frac{5R}{36} $ (for $n_i=3$) and $ \frac{3R}{16} $ (for $n_i=4$).
- Step 4: Evaluate the given options. Option C is $ \frac{3\text{R}}{4}, \frac{3\text{R}}{16}, \frac{7\text{R}}{144} $. This set includes $ \frac{3R}{16} $, which is a valid Balmer line. This option is selected as the correct set.
Similar Questions
Assuming in forward bias condition there is a voltage drop of $0.7 \text{ V}$ across a silicon diode, the current through diode $D_1$ in the circuit is ________$\text{mA}$.
(Assume all diodes in the given circuit are identical)
- The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with kinetic energy $2E$, is $n : 1$. The value of $n$ is ________.
(Assume mass of proton = mass of neutron) : - 7.9 MeV $\alpha$-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) _________ m.
$\left[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2 \text{ and electron charge} = 1.6 \times 10^{-19} \text{ C} \right]$ Find the correct combination of A, B, C and D inputs which can cause the LED to glow.
- The minimum frequency of photon required to break a particle of mass 15.348 amu into 4 $\alpha$ particles is _________ kHz.
[mass of He nucleus = 4.002 amu, $1 \text{ amu} = 1.66 \times 10^{-27} \text{ kg}, h = 6.6 \times 10^{-34} \text{ J.s} \text{ and } c = 3 \times 10^8 \text{ m/s}$] The correct truth table for the given input data of the following logic gate is :
- Light is incident on a metallic plate having work function $110 \times 10^{-20} \text{ J}$. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is _________ rad/s.
(h = $6.63 \times 10^{-34} \text{ J.s}$). - The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly _________ nm.
- Two electrons are moving in orbits of two hydrogen like atoms with speeds $3 \times 10^5 \text{ m/s}$ and $2.5 \times 10^5 \text{ m/s}$ respectively. If the radii of these orbits are nearly same then the possible order of energy states are ______ respectively.
- Given below are two statements:
Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement II: For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon.
In the light of the above statements, choose the correct answer from the options given below
Important Questions from Modern Physics
Assuming in forward bias condition there is a voltage drop of $0.7 \text{ V}$ across a silicon diode, the current through diode $D_1$ in the circuit is ________$\text{mA}$.
(Assume all diodes in the given circuit are identical)- The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with kinetic energy $2E$, is $n : 1$. The value of $n$ is ________.
(Assume mass of proton = mass of neutron) : - 7.9 MeV $\alpha$-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) _________ m.
$\left[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2 \text{ and electron charge} = 1.6 \times 10^{-19} \text{ C} \right]$ Find the correct combination of A, B, C and D inputs which can cause the LED to glow.
- The minimum frequency of photon required to break a particle of mass 15.348 amu into 4 $\alpha$ particles is _________ kHz.
[mass of He nucleus = 4.002 amu, $1 \text{ amu} = 1.66 \times 10^{-27} \text{ kg}, h = 6.6 \times 10^{-34} \text{ J.s} \text{ and } c = 3 \times 10^8 \text{ m/s}$]
