Which of the following does not represent the mathematical expression for the Heisenberg uncertainty principle? 

1. $∆x.∆p\ge \frac{h}{4\mathrm{\pi }}$

2. $∆x.∆v\ge \frac{h}{4\mathrm{\pi m}}$

3. $∆E.∆t\ge \frac{h}{4\mathrm{\pi }}$

4. $∆E.∆x\ge \frac{h}{4\mathrm{\pi }}$

The wavelength associatedd with a golf ball weighing 200 g and moving at a speed of 5 m/h is of the order:

(1) ${10}^{-10}<mspace\; width="1em"></mspace>m$

(2) ${10}^{-20}<mspace\; width="1em"></mspace>m$

(3) ${10}^{-30}<mspace\; width="1em"></mspace>m$

(4) ${10}^{-40}<mspace\; width="1em"></mspace>m$

The energy of an electron in the first Bohr's orbit of an H-atom is -13.6 eV. The possible energy value (s) of the excited state(s) for electrons in Bohr's orbits of hydrogen is (are):

1. -3.4 eV

2. -4.2 eV

3. -6.8 eV

4. +6.8 eV

In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inter orbit jumps of the electron for Bohr's orbits in an atom of hydrogen?

(1) $3\to 2$

(2) $5\to 2$

(3) $4\to 1$

(4) $2\to 5$

The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 metres per second is approximate- 

(Planck's constant, $h=6.63\times {10}^{-34}<mspace\; width="1em"></mspace>Js$)

1. ${10}^{-33}$ metres

2. ${10}^{-31}$ metres

3. ${10}^{-16}$ metres

4. ${10}^{-25}$ metres

Which of the following ions has the same radius as the first Bohr orbit of the hydrogen atom?

1. ${\mathrm{He}}^{+},$ $n=2$

2. ${\mathrm{Li}}^{2+},n=2$

3. ${\mathrm{Be}}^{3+},$ $n=2$

4. ${\mathrm{Li}}^{2+},\mathrm{n}=3$

The number of electrons with the azimuthal quantum number l = 1 and 2 for Cr ₂₄ in ground state is

1. 16 and 5

2. 12 and 5

3. 16 and 4

4. 12 and 4

The wavelength of the radiation emitted when in a H atom, the electron falls from infinity to stationary state (n=1), is:

1. $15$ $nm$

2. 192 nm

3. 406 nm

4. 91 nm

The number of radial nodes of 3s and 2p-orbitals are respectively:

(1) 2,0

(2) 0,2

(3) 1,2 

(4) 2,1

A macroscopic particle of mass \(100 ~\text g \) and moving at a velocity of \(100~ \text {cm} ~\text s^{–1}\) will have a de broglie wavelength of:

1. 6.6 × 10^–29 cm 

2. 6.6 × 10^–30 cm 

3. 6.6 × 10^–31 cm 

4. 6.6 × 10^–32 cm