The de Broglie wavelength associated with a ball of mass 1 ~kg having kinetic energy 0.5 ~J is

Correct answer: A. 6.626 × 10^ -34 ~m Kinetic energy =(1)/(2) m v^2 [m=mass, v= velocity ] or, 0.5=(1)/(2) × 1 × v^2 or, v=1 ~ms^ -1 . de Broglie wavelength, λ=(h)/(m v) or, λ= 6.626 × 10^ -34 Js 1 ~kg × 1 ~ms^ -1 =6.626 × 10^ -34 ~m .

AIIMS 2006

Exam: AIIMS
Year: 2006
Subject: Chemistry
Chapter: Structure of Atom

AIIMS 2006 · Chemistry · Structure of Atom

The de Broglie wavelength associated with a ball of mass 1 ~kg...

The de Broglie wavelength associated with a ball of mass

1 \mathrm{~kg}

having kinetic energy

0.5 \mathrm{~J}

Options

A $6.626 \times 10^{-34} \mathrm{~m}$
B $13.20 \times 10^{-34} \mathrm{~m}$
C $10.38 \times 10^{-21} \mathrm{~m}$
D $6.626 \times 10^{-34} A$ .

Correct answer

A. $6.626 \times 10^{-34} \mathrm{~m}$

Step-by-step solution

Kinetic energy

=\frac{1}{2} m v^2\text{ [m=mass, }

\text{ velocity }]

or,

0.5=\frac{1}{2} \times 1 \times v^2

or,

v=1 \mathrm{~ms}^{-1}

. de Broglie wavelength,

\lambda=\frac{h}{m v}

or,

\lambda=\frac{6.626 \times 10^{-34} \mathrm{Js}}{1 \mathrm{~kg} \times 1 \mathrm{~ms}^{-1}}=6.626 \times 10^{-34} \mathrm{~m}

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