1
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1

If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is _________ nm. (Nearest integer)

2
JEE Main 2022 (Online) 29th July Morning Shift
Numerical
+4
-1

The minimum uncertainty in the speed of an electron in an one dimensional region of length $$2 \mathrm{a}_{\mathrm{o}}$$ (Where $$\mathrm{a}_{\mathrm{o}}=$$ Bohr radius $$52.9 \,\mathrm{pm}$$) is _________ $$\mathrm{km} \,\mathrm{s}^{-1}$$.

(Given : Mass of electron = 9.1 $$\times$$ 10$$-$$31 kg, Planck's constant h = 6.63 $$\times$$ 10$$-$$34 Js)

3
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1

If the wavelength for an electron emitted from $$\mathrm{H}$$-atom is $$3.3 \times 10^{-10} \mathrm{~m}$$, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is _________ times. (Nearest integer)

$$\left[\right.$$ Given $$: \mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s}$$ ]

Mass of electron $$=9.1 \times 10^{-31} \mathrm{~kg}$$

4
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1

Consider an imaginary ion $${ }_{22}^{48} \mathrm{X}^{3-}$$. The nucleus contains '$$a$$'% more neutrons than the number of electrons in the ion. The value of 'a' is _______________. [nearest integer]