Question:
The following parameter is same for all hydrogen like atoms and ions in their ground state.
The following parameter is same for all hydrogen like atoms and ions in their ground state.
Show Hint
For hydrogen-like atoms, radius, speed and energy depend on atomic number \(Z\), but angular momentum is quantized as
\[
L=\frac{nh}{2\pi}.
\]
For ground state, \(n=1\), so \(L=\dfrac{h}{2\pi}\).
Updated On: Jun 18, 2026
- Radius of the orbit
- Speed of the electron
- Energy of the atom
- Orbital angular momentum of the electron
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Recall Bohr's quantization condition.
According to Bohr's model, \[ mvr=\frac{nh}{2\pi} \] where \(n\) is the principal quantum number.
Step 2: Apply ground state condition.
For ground state, \[ n=1 \] Therefore, \[ mvr=\frac{h}{2\pi} \] This value does not depend on atomic number \(Z\).
Step 3: Check other quantities.
For hydrogen-like species, \[ r_n\propto \frac{n^2}{Z} \] so radius depends on \(Z\).
Also, \[ v_n\propto \frac{Z}{n} \] so speed depends on \(Z\).
Energy is \[ E_n\propto -\frac{Z^2}{n^2} \] so energy also depends on \(Z\).
Step 4: Final conclusion.
Hence, only orbital angular momentum is same for all hydrogen-like atoms and ions in the ground state. \[ \boxed{\text{Orbital angular momentum of the electron}} \]
According to Bohr's model, \[ mvr=\frac{nh}{2\pi} \] where \(n\) is the principal quantum number.
Step 2: Apply ground state condition.
For ground state, \[ n=1 \] Therefore, \[ mvr=\frac{h}{2\pi} \] This value does not depend on atomic number \(Z\).
Step 3: Check other quantities.
For hydrogen-like species, \[ r_n\propto \frac{n^2}{Z} \] so radius depends on \(Z\).
Also, \[ v_n\propto \frac{Z}{n} \] so speed depends on \(Z\).
Energy is \[ E_n\propto -\frac{Z^2}{n^2} \] so energy also depends on \(Z\).
Step 4: Final conclusion.
Hence, only orbital angular momentum is same for all hydrogen-like atoms and ions in the ground state. \[ \boxed{\text{Orbital angular momentum of the electron}} \]
Was this answer helpful?
0
0
Top AP EAPCET Chemistry Questions
- The four quantum numbers of the valence electron of potassium are :
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
- In which of the following the election gain enthalpy of elements is correctly arranged?
- The radii of $ \text{F,}{{\text{F}}^{-}}\text{O} $ and $ {{\text{O}}^{2-}} $ are in the order
- Which of the following has the highest first ionization potential?
View More Questions
Top AP EAPCET Bohr's model of hydrogen atom Questions
- According to Bohr's model, the angular momentum of an electron in a stable orbit is an integral multiple of
- The difference between the radii of M and N shells of $He^+$ is $\Delta R_1$(nm). The difference between the radii of L and N shells of $Li^{2+}$ is $\Delta R_2$(nm). The ratio of $\Delta R_1$ to $\Delta R_2$ is:
- If the velocity of an electron in the first Bohr's orbit of H-atom is x $ms^{-1}$, then the velocity (in $ms^{-1}$) of an electron in the fourth Bohr's orbit of the same atom is:
- A radiation of energy 11.0 eV is irradiated on gaseous hydrogen atoms at room temperature. Identify the energy level to which electron of hydrogen atom can be excited:
- The value of Rydberg constant in J is:
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions