Match the equations given in List-$I$ with their names in List-$II$.
List-$I$ List-$II$ $(1)$ $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$ $(A)$ De Broglie equation $(2)$ $mvr \ge \frac{nh}{2\pi}$ $(B)$ Uncertainty principle $(3)$ $\lambda = \frac{h}{\sqrt{2m(KE)}}$ $(C)$ Frequency equation of $H$-spectrum $(4)$ $\nu = 3.29 \times 10^{15} \left( \frac{1}{n_i^2} - \frac{1}{n_f^2} \right)$ $(D)$ Angular momentum is quantized
| List-$I$ | List-$II$ |
| $(1)$ $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$ | $(A)$ De Broglie equation |
| $(2)$ $mvr \ge \frac{nh}{2\pi}$ | $(B)$ Uncertainty principle |
| $(3)$ $\lambda = \frac{h}{\sqrt{2m(KE)}}$ | $(C)$ Frequency equation of $H$-spectrum |
| $(4)$ $\nu = 3.29 \times 10^{15} \left( \frac{1}{n_i^2} - \frac{1}{n_f^2} \right)$ | $(D)$ Angular momentum is quantized |
(B) The correct matches are:
$(1)$ $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$ is the Heisenberg Uncertainty Principle $(B)$.
$(2)$ $mvr = \frac{nh}{2\pi}$ represents the quantization of angular momentum $(D)$.
$(3)$ $\lambda = \frac{h}{\sqrt{2m(KE)}}$ is the De Broglie equation relating wavelength to kinetic energy $(A)$.
$(4)$ $\nu = 3.29 \times 10^{15} \left( \frac{1}{n_i^2} - \frac{1}{n_f^2} \right)$ is the Rydberg frequency equation for the $H$-spectrum $(C)$.
Therefore,the correct sequence is $(1-B, 2-D, 3-A, 4-C)$.
$(1)$ $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$ is the Heisenberg Uncertainty Principle $(B)$.
$(2)$ $mvr = \frac{nh}{2\pi}$ represents the quantization of angular momentum $(D)$.
$(3)$ $\lambda = \frac{h}{\sqrt{2m(KE)}}$ is the De Broglie equation relating wavelength to kinetic energy $(A)$.
$(4)$ $\nu = 3.29 \times 10^{15} \left( \frac{1}{n_i^2} - \frac{1}{n_f^2} \right)$ is the Rydberg frequency equation for the $H$-spectrum $(C)$.
Therefore,the correct sequence is $(1-B, 2-D, 3-A, 4-C)$.
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Consider the following:
$I$. The electron spin quantum number describes the orientation of the spin of the nucleus with respect to the magnetic field.
$II$. The orbitals represented by the quantum numbers $n=3, l=2, m=+2$ and $n=3, l=2, m=-2$ have the same energy.
$III$. The energy of a photon is directly proportional to wavelength but inversely proportional to wave number.
$IV$. Lyman series of lines appear in ultra-violet region.
The correct statements are:
$I$. The electron spin quantum number describes the orientation of the spin of the nucleus with respect to the magnetic field.
$II$. The orbitals represented by the quantum numbers $n=3, l=2, m=+2$ and $n=3, l=2, m=-2$ have the same energy.
$III$. The energy of a photon is directly proportional to wavelength but inversely proportional to wave number.
$IV$. Lyman series of lines appear in ultra-violet region.
The correct statements are:
In the transition of an electron in an atom,its kinetic energy changes from $y$ to $y/4$. The change in $P.E.$ will be
Medium
View SolutionIdentify the correct statements from the following:
$A$. Heisenberg uncertainty principle is applicable to electrons.
$B$. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital.
$C$. The energy of $2s$ orbital of $H$ atom is equal to the energy of $2s$ orbital of $Li$.
$D$. The electronic configuration of $Cr$ is $[Ar]3d^5 4s^1$.
$A$. Heisenberg uncertainty principle is applicable to electrons.
$B$. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital.
$C$. The energy of $2s$ orbital of $H$ atom is equal to the energy of $2s$ orbital of $Li$.
$D$. The electronic configuration of $Cr$ is $[Ar]3d^5 4s^1$.
When the excited electron of a $H$ atom from $n=5$ drops to the ground state,the maximum number of emission lines observed are $.......$
What is the ratio of time periods in the $3^{rd}$ orbit of $H^{-}$ atom to the $2^{nd}$ orbit of $He^{+}$ ion?
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