De-Broglie wavelength of an electron orbiting in the \(n=2\) state of a hydrogen atom is close to: (given: Bohr radius \(=0.052~ \text{nm}\))
| 1. | \(1.67~ \text{nm}\) | 2. | \(2.67~ \text{nm}\) |
| 3. | \(0.067~ \text{nm}\) | 4. | \(0.67~ \text{nm}\) |
Subtopic: De-broglie Wavelength |
Level 3: 35%-60%
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A photon and an electron (of mass \(m\)) have the same total energy \(E. \) If \(c\) denotes the speed of light, what is the ratio of their de-Broglie wavelengths \((\lambda_{\text{photon}}/\lambda_{\text{electron}})\text{?} \)
| 1. | \(c\sqrt{\dfrac{2m}{E}} \) | 2. | \(\dfrac{1}{c}\sqrt{\dfrac{E}{2m}}\) |
| 3. | \(\sqrt{\dfrac{E}{2m}}\) | 4. | \(c\sqrt{2mE}\) |
Subtopic: De-broglie Wavelength |
Level 3: 35%-60%
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A particle of mass \(m\) is moving around the origin with a constant force \(F\) pulling it towards the origin. If Bohr model is used to describe its motion, the radius \(r\) of the \(n^{\text{th}}\) orbit and the particle's speed \(v\) in the orbit depend on \(n\) as:
| 1. | \(r \propto n^{2/3}; v \propto n^{1/3}\) | 2. | \(r \propto n^{4/3}; v \propto n^{-1/3}\) |
| 3. | \(r \propto n^{1/3}; v \propto n^{1/3}\) | 4. | \(r \propto n^{1/3}; v \propto n^{2/3}\) |
Subtopic: Bohr's Model of Atom |
Level 3: 35%-60%
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A full wave rectifier circuit with diodes \((D_1)\) and \((D_2)\) is shown in the figure. If input supply voltage \(V_{\text{in}}=220\sin(100\pi t)\) volt, then at \(t=15~\text{ms}\text{:}\)
| 1. | \(D_1\) and \(D_2\) both are forward biased |
| 2. | \(D_1\) and \(D_2\) both are reverse biased |
| 3. | Neither \(D_1\) nor \(D_2\) conducts at any time |
| 4. | \(D_1\) is reverse biased, \(D_2\) is forward biased |
Subtopic: Rectifier |
Level 3: 35%-60%
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The output \(Y \) of the given logic implementation is similar to the output of which gate?
| 1. | OR | 2. | NOR |
| 3. | AND | 4. | NAND |
Subtopic: Logic gates |
Level 3: 35%-60%
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Atomic theory could not explain which of the following?
| 1. | Law of multiple proportion | 2. | Law of gaseous volume |
| 3. | Law of conservation of mass | 4. | Law of constant proportion |
Subtopic: Introduction |
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Level 2: 60%+
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Consider the following data of compounds:
Which of the following represents a correct set of compounds having an equal number of atoms?
| A. | \(212 ~g ~\text{of}~Na_2CO_3 (s) \text{[molar mass}=106 ~g]\) |
| B. | \(~248 g ~\text{of}~ {Na}_2 \mathrm{O}({s}) [\text{molar mass} =62 \mathrm{~g} ]\) |
| C. | \(240 g ~\text{of} ~NaOH (s)~ [\text{molar mass} =40 \mathrm{~g} \) |
| D. | \( 12 g~ \text{of}~ \mathrm{H}_2(\mathrm{~g})[ \text{molar mass} =2 \mathrm{~g}].\) |
| E. | \( 220 g~ \text{of} ~\mathrm{CO}_2(\mathrm{~g})[\text{ molar mass }=44 \mathrm{~g}]\) |
| 1. | B, C, and D only | 2. | B, D, and E only |
| 3. | A, B, and C only | 4. | A, B, and D only |
Subtopic: Moles, Atoms & Electrons |
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Level 3: 35%-60%
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The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes \(n=2 \rightarrow n=3\) and \(n=4 \rightarrow n=6\) transitions, respectively, is
| 1. | \(\dfrac{1}{9}\) | 2. | \(\dfrac{1}{4}\) |
| 3. | \(\dfrac{1}{36}\) | 4. | \(\dfrac{1}{16}\) |
Subtopic: Hydrogen Spectra |
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Level 2: 60%+
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Energy and radius of the first Bohr orbit of He+ and Li2+ are: [Given \(\left.\mathrm{R}_{\mathrm{H}}=2.18 \times 10^{-18} \mathrm{~J}, \mathrm{a}_0=52.9 \mathrm{pm}\right]\)
| 1. | \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-19.62 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6\mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=8.72 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=26.4 \mathrm{pm} \end{aligned}\) |
| 2. | \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-8.72 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-19.62 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=17.6 \mathrm{pm} \end{aligned}\) |
| 3. | \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=- 19.62 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-8.72 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=26.4 \mathrm{pm} \end{aligned}\) |
| 4. | \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-8.72 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=26.4 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-19.62 \times 10^{-18} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=17.6 \mathrm{pm} \end{aligned} \) |
Subtopic: Bohr's Theory |
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Level 2: 60%+
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Which of the following electronic configurations belong to the main group elements?
Choose the correct answer from the option given below:
| A | \([\mathrm{Ne}] 3 \mathrm{~s}^1\) | B | \([\mathrm{Ar}] 3d^3 \mathrm{~4s}^2\) |
| C | \([\mathrm{Kr}] 4 \mathrm{~d}^{10} 5 \mathrm{~s}^2 5 \mathrm{p}^5\) | D | \([\mathrm{Ar}] 3 \mathrm{~d}^{10} 4 \mathrm{~s}^1\) |
| E | \(\mathrm{[R n] }5 f^0 6 d^2 7 s^2\) | ||
Choose the correct answer from the option given below:
| 1. | D and E only | 2. | A, C and D only |
| 3. | B and E only | 4. | A and C only |
Subtopic: Modern Periodic Table & Periodicity |
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Level 3: 35%-60%
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