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Q1:

Energy and radius of the first Bohr orbit of $He^+$ and $Li^{2+}$ 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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Q2:

The energy of electron in the ground state $(\text{n}=1)$ for $\text{He}^+$ ion is $\text{-x}J,$ then that for an electron in $\text{n}=2$ state for $\text{Be}^{3+}$ ion in $\text{J}$ is :

1.	$-\dfrac x9$	2.	$-4x$
3.	$-\dfrac 49x$	4.	$-x$

Subtopic: Bohr's Theory |

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NEET - 2024

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Q3:

Given below are two statement:

Statement I:	The energy of the $\mathrm{He}^{+}$ ion in $n=2$ state is same as the energy of H atom in $n=1$ state
Statement II:	It is possible to determine simultaneously the exact position and exact momentum of an electron in $\mathrm{H}$ atom.

In the light of the above Statements, choose the correct answer from the options given below:
1. Both Statement I and Statement II are True
2. Both Statement I and Statement II are False
3. Statement I is True but Statement II is False
4. Statement I is False but Statement II is True

Subtopic: Bohr's Theory | Heisenberg Uncertainty Principle |

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Q4:

Given below are two statements:

Statement I:	The Balmer spectral line for H atom with lowest energy appears at $\dfrac 5{36}\mathrm{ R_H~ cm^{-1}}$ ($\mathrm{R_H}$ = Rydberg constant)
Statement II:	When the temperature of a black body increases, the maxima of the curve (intensity versus wavelength) shifts towards shorter wavelength.

In the light of the above statements, choose the correct answer from the options given below:

1.	Statement I is correct and Statement II is incorrect.
2.	Statement I is incorrect and Statement II is correct.
3.	Both Statement I and Statement II are correct.
4.	Both Statement I and Statement II are incorrect.

Subtopic: Bohr's Theory | Planck's Theory |

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Q5:

In hydrogen atom, what is the de Broglie wavelength of an electron in the second Bohr orbit is: [Given that Bohr radius, $a_{0} = 52.9$ $p m$ ]

1. 211.6 pm

2. 211.6 $π$ pm

3. $52.9$ $π$ pm

4. 105.8 pm

Subtopic: Bohr's Theory |

NEET - 2019

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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.	\(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-8.72 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=26.4 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-19.62 \times 10^{-18} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=17.6 \mathrm{pm} \end{aligned} \)

Statement I:	The energy of the \(\mathrm{He}^{+}\) ion in \(n=2\) state is same as the energy of H atom in \(n=1\) state
Statement II:	It is possible to determine simultaneously the exact position and exact momentum of an electron in \(\mathrm{H}\) atom.

1.	\(-\dfrac x9\)	2.	\(-4x\)
3.	\(-\dfrac 49x\)	4.	\(-x\)

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