Question

why Alpha particle have a wavelength 7344 times smaller as compared to that of electron?​

Answer 1

Answer:

Kinetic energy is given by E=21mv2

Same kinetic energy implies that electron has highest velocity (as mass is lowest). 

Assume mass of electron as 1 unit. Now, mass of proton approx 1836 and mass of alpha particle is 4 times that is 7344.

Now calculate velocity in each case

For electron v=2E, proton v=18362E and alpha particle v=73442E

Also de-Broglie wavelength is given by λ=mvh

Now calculate momentum in each case

For electron mv=2E×1  proton mv=18362E×1836 and alpha particle mv=73442E×7344

Clearly electron has least momentum. Hence it has largest de-Broglie wavelength. And Alpha particle has least wavelength

Answer 2

Kinetic energy is given by E=

2

1

mv

2

Same kinetic energy implies that electron has highest velocity (as mass is lowest).

Assume mass of electron as 1 unit. Now, mass of proton approx 1836 and mass of alpha particle is 4 times that is 7344.

Now calculate velocity in each case

For electron v=

2E

, proton v=

1836

2E

and alpha particle v=

7344

2E

Also de-Broglie wavelength is given by λ=

mv

h

Now calculate momentum in each case

For electron mv=

2E

×1 proton mv=

1836

2E

×1836 and alpha particle mv=

7344

2E

×7344

Clearly electron has least momentum. Hence it has largest de-Broglie wavelength. And Alpha particle has least wavelength.

Hope it helps. Please mark me BRAINLIEST.