Question

Two particles A and B are in motion. If the wavelength
associated with particle A is 5 × 10-8 m; calculate
the wavelength associated with particle B if its
momentum is half of A.
(1) 5 x 10-8 m (2) 10-5 cm
(3) 10-7cm
(4) 5 x 10-8 cm​

Answer 1

Answer:

Wavelength of the particle A = 5 x 10^-8 m

Let the momentum of particle A is pA and the momentum of the particle B is pB

Relation between pA and pB is :

pB = pA/2

pA = h/ 5 x 10^-8 m

pB = h/ 5 x 10^-8 m x 2

Wavelength of B(lambda) = h/pB

                    = h/ [h/ (5 x 10^-8 m) x 2]

                    = 10 x 10-8 m

                    = 10^-7 m

Answer 2

The wavelength associated with particle B if its

momentum is half of A is 10-7 cm.

Explanation:

• Calculated the wavelength (in A˚) associated with particle B if its momentum is half of A.
• One wavelength equals the distance between two successive wave crests or troughs.
• Momentum is inversely proportional to wavelength .
• By de Broglie equation, λA = h/pA and λ = h/pB

                                               ∴ λA/λB = pB/pA

                                               But, pB = 1/2pA (Given)

                                               λAλB = 1/2pA/pA = 12

                                                        (or)

                                                λB = 2×λA = 2×5×10−8m = 10−7m.

To Learn More...

1.Two particles A and B are in motion. If the wavelength associated with particle A is 5x10^-8m, calculate wavelength associated with B if its momentum is half of A

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