KCET · Physics · Dual Nature of Matter
Angular momentum of an electron in hydrogen atom is \(\frac{3 h}{2 \pi}(h\) is the Planck's constant). The KE of the electron is
- A \(4.35 \mathrm{eV}\)
- B \(1.51 \mathrm{eV}\)
- C \(3.4 \mathrm{eV}\)
- D \(6.8 \mathrm{eV}\)
Answer & Solution
Correct Answer
(B) \(1.51 \mathrm{eV}\)
Step-by-step Solution
Detailed explanation
Given, angular momentum of electron in
H-atom \(=\frac{3 h}{2 \pi}...(i)\)
From Bohr's postulate,
Angular momentum \(=\frac{n h}{2 \pi}...(ii)\)
Comparing Eqs. (i) and (ii), we get
\(n=3\)
The kinetic energy of an electron in hydrogen is given by
\(\begin{aligned}
\mathrm{KE} &=\frac{13.6 \times Z^{2}}{n^{2}} \mathrm{eV} \\
&=\frac{13.6 \times 1}{3^{2}} \\
&=1.51 \mathrm{eV}
\end{aligned}\)
\((\) for \(H, Z=1\) )
H-atom \(=\frac{3 h}{2 \pi}...(i)\)
From Bohr's postulate,
Angular momentum \(=\frac{n h}{2 \pi}...(ii)\)
Comparing Eqs. (i) and (ii), we get
\(n=3\)
The kinetic energy of an electron in hydrogen is given by
\(\begin{aligned}
\mathrm{KE} &=\frac{13.6 \times Z^{2}}{n^{2}} \mathrm{eV} \\
&=\frac{13.6 \times 1}{3^{2}} \\
&=1.51 \mathrm{eV}
\end{aligned}\)
\((\) for \(H, Z=1\) )
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A proton, a deuteron and an \( \alpha \) - particle are projected perpendicular to the direction of a
uniform magnetic field with same kinetic energy. The ratio of the radii of the circular paths
described by them isKCET 2017 Medium - Consider a glass slab which is silvered at one side and the other side is transparent. Given the refractive index of the glass slab to be 1.5. If a ray of light is incident at an angle of \(45^{\circ}\) on the transparent side, then the deviation of the ray of light from its initial path, when it comes out of the slab isKCET 2022 Hard
- The deflection in a moving coil galvanometer is reduced to half when it is shunted with a \(40 \Omega\) coil. The resistance of the galvanometer isKCET 2011 Easy
- The component of a vector \( \vec{r} \) along \( x \) - axis will have a maximum value ifKCET 2016 Easy
- A ray of light passes from vaccum into a medium of refractive index \(n\). If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index isKCET 2025 Medium
- Two tangent galvanometers \(A\) and \(B\) have coils of radii \(8 \mathrm{~cm}\) and \(16 \mathrm{~cm}\) respectively and resistance \(8 \Omega\) each. They are connected in parallel with a cell of emf \(4 \mathrm{~V}\) and negligible internal resistance. The deflections produced in the tangent galvanometers \(A\) and \(B\) are \(30°\) and \(60°\) respectively. If A has 2 turns, then B must haveKCET 2007 Hard
More PYQs from KCET
- The colour of sky is due toKCET 2008 Easy
- For the arrangement of capacitors as shown in the circuit, the effective capacitance between the points \( A \) and \( B \) is (capacitance of each capacitor is \( 4 \mu \mathrm{F} \) )
KCET 2018 Medium - Identify the hormones 'A', 'B' and 'C' that are labelled in the given flow chart.
KCET 2014 Hard - Two circles centred at \((2,3)\) and \((5,6)\) intersect each other. If the radii are equal, the equation of the common chord isKCET 2010 Medium
- The component of \(\mathbf{i}\) in the direction of the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) isKCET 2023 Easy
- If \(\overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}=\overrightarrow{\mathbf{a}} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}})=\overrightarrow{\mathbf{a}} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})=1\) then \(\overrightarrow{\mathbf{a}}\) is equal toKCET 2008 Medium