<u>Answer:</u>
<u>For a:</u> The De-Broglie wavelength of the given particle is
<u>For b:</u> The uncertainty in the position is
<u>Explanation:</u>
To calculate the wavelength of a particle, we use the equation given by De-Broglie's wavelength, which is:
where,
= De-Broglie's wavelength = ?
h = Planck's constant =
m = mass of the alpha particle =
v = velocity of alpha particle = (Conversion factors used: 1 mile = 1609.34 m & 1 hr = 3600 s)
Putting values in above equation, we get:
Hence, the De-Broglie wavelength of the given particle is
The equation representing Heisenberg's uncertainty principle follows:
where,
= uncertainty in position = ?
= uncertainty in momentum =
m = mass of the alpha particle =
= uncertainty in speed =
h = Planck's constant =
Putting values in above equation, we get:
Hence, the uncertainty in the position is