1
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
A particle of mass m moves in circular orbits with potential energy V(r) = Fr, where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle’s orbit is denoted by R and its speed and energy are denoted by v and E, respectively, then for the nth orbit (here h is the Planck’s constant)
A
$$R \propto {n^{{1 \over 3}}}$$ and $$v \propto {n^{{2 \over 3}}}$$
B
$$R \propto {n^{{2 \over 3}}}$$ and $$v \propto {n^{{1 \over 3}}}$$
C
$$E = {3 \over 2}{\left( {{{{n^2}{h^2}{F^2}} \over {4{\pi ^2}m}}} \right)^{{1 \over 3}}}$$
D
$$E = 2{\left( {{{{n^2}{h^2}{F^2}} \over {4{\pi ^2}m}}} \right)^{{1 \over 3}}}$$
2
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
A free hydrogen atom after absorbing a photon of wavelength $$\lambda $$a gets excited from the state n = 1 to the state n = 4. Immediately after that the electron jumps to n = m state by emitting a photon of wavelength $$\lambda $$e. Let the change in momentum of atom due to the absorption and the emission be $$\Delta {p_a}$$ and $$\Delta {p_e}$$, respectively. If $${{{\lambda _a}} \over {{\lambda _e}}} = {1 \over 5}$$, which of the option(s) is/are correct? [Use hc = 1242 eVnm; 1 nm = 10-9 m, h and c are Planck's constant and speed of light in vacuum, respectively]
A
The ratio of kinetic energy of the electron in the state n = m to the state, n = 1 is $${1 \over 4}$$
B
m = 2
C
$${{\Delta {p_a}} \over {\Delta {p_e}}} = {1 \over 2}$$
D
$$\lambda $$e = 418 nm
3
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Change Language
In a radioactive decay chain, $${}_{90}^{232}Th$$ nucleus decays to $${}_{82}^{212}Pb$$ nucleus. Let $${N_\alpha }$$ and $${N_\beta }$$ be the number of $$\alpha $$ and $${\beta ^ - }$$ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?
A
$${N_\alpha } = 5$$
B
$${N_\alpha } = 6$$
C
$${N_\beta } = 2$$
D
$${N_\beta } = 4$$
4
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n, where n >> 1. Which of the following statement(s) is(are) true?
A
Relative change in the radii of two consecutive orbitals does not depend on Z.
B
Relative change in the radii of two consecutive orbitals varies as 1/n
C
Relative change in the energy of two consecutive orbitals varies as 1/n3
D
Relative change in the angular momenta of two consecutive orbitals varies as 1/n
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