Dual nature of matter; de Broglie relation; uncertainty principle — practice questions

Question 1 · difficulty L2 · understanding

The de-Broglie's wavelength of an electron in the $$4^{\text {th }}$$ orbit is ________ $$\pi \mathrm{a}_0$$. ($$\mathrm{a}_0=$$ Bohr's radius)

Question 2 · difficulty L2 · understanding

If the uncertainty in velocity and position of a minute particle in space are, 2.4 $$\times$$ 10 $$-$$26 (m s $$-$$1 ) and 10 $$-$$7 (m) respectively. The mass of the particle in g is ____________. (Nearest integer) (Given : h = 6.626 $$\times$$ 10 $$-$$34 Js)

Question 3 · difficulty L2 · understanding

A ball weighing 10 g is moving with a velocity of 90 ms $$-$$1 . If the uncertainty in its velocity is 5%, then the uncertainty in its position is ___________ $$\times$$ 10 $$-$$33 m. (Rounded off to the nearest integer) [Given : h = 6.63 $$\times$$ 10 $$-$$34 Js]

Question 4 · difficulty L2 · understanding

If $a$ 0 is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present in the second orbit of hydrogen atom? [n : any integer]

• A. $\frac{8 \pi a_0}{n}$
• B. $\frac{2 a_0}{n \pi}$
• C. $\frac{n a_0}{4 \pi}$
• D. $\frac{4 \pi a_0}{n}$

Question 5 · difficulty L3 · understanding

Two positively charged particles $m_1$ and $m_2$ have been accelerated across the same potential difference of 200 keV as shown below. [Given mass of $m_1 = 1$ amu and $m_2 = 4$ amu] The deBroglie wavelength of $m_1$ will be $x$ times of $m_2$. The value of $x$ is __________ (nearest integer)

Question 6 · difficulty L3 · understanding

Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter $$10^{-15} \mathrm{~m}$$ is ________ $$\times 10^9 \mathrm{~ms}^{-1}$$ (nearest integer) [Given : mass of electron $$=9.1 \times 10^{-31} \mathrm{~kg}$$, Plank's constant $$(h)=6.626 \times 10^{-34} \mathrm{Js}$$] (Value of $$\pi=3.14$$)

Question 7 · difficulty L3 · understanding

Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _________ $$\times 10^{13} \mathrm{~Hz}$$ (nearest integer). [Given : $$\mathrm{R}_{\mathrm{H}}$$ (Rydberg constant) $$=2.18 \times 10^{-18} \mathrm{~J}, h$$ (Plank's constant) $$=6.6 \times 10^{-34} \mathrm{~J} . \mathrm{s}$$.]

Question 8 · difficulty L3 · understanding

Electrons in a cathode ray tube have been emitted with a velocity of 1000 m s$$^{-1}$$. The number of following statements which is/are $$\underline {\mathrm{true}}$$ about the emitted radiation is ____________. Given : $$\mathrm{h=6\times10^{-34}~J~s,m_e=9\times10^{-31}~kg}$$. (A) The de-Broglie wavelength of the electron emitted is 666.67 nm. (B) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube. (C) The cathode rays start from cathode and move towards anode. (D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube.

Question 9 · difficulty L3 · understanding

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)

Question 10 · difficulty L3 · understanding

An accelerated electron has a speed of 5 $$\times$$ 10 6 ms $$-$$1 with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is x $$\times$$ 10 $$-$$9 m. The value of x is ____________. (Nearest integer) [Use mass of electron = 9.1 $$\times$$ 10 $$-$$31 kg, h =6.63 $$\times$$ 10 $$-$$34 Js, $$\pi$$ = 3.14]