Question
Compare the de Broglie wavelength of an alpha particle moving at 3.40 times 10^7 miles per hour (1.52 times 10^7 mathrm(m) / mathrm(s) ) to that of a baseball moving at 90.0 miles per hour (40.2 mathrm(~m) / mathrm(s)) and an electron with a speed of 1.30 times 10^7 miles per hour (5.81 times 10^6 mathrm(~m) / mathrm(s)) . Particle & Mass (kg) & }(c) Velocity (mathrm(m) / mathrm(s)) & Wavelength & Region alpha particle & & baseball & 0.140 & 40.2 & 1.175 times 10^wedge-34 & smaller than 10^-20 mathrm(~m) electron & 9.11 times 10^-31 & 5.81 times 10^6 & &
Answer
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Ava
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Answer
1. The de Broglie wavelength of an alpha particle is significantly smaller than that of a baseball.2. The de Broglie wavelength of an electron is significantly larger than that of a baseball.
Explanation
## Step 1:The de Broglie wavelength of a particle is given by the formula:###
where
is Planck's constant (
) and
is the momentum of the particle. The momentum is calculated as the product of mass and velocity.## Step 2:For an alpha particle with a mass of
and a velocity of
, the de Broglie wavelength will be:###
## Step 3:For a baseball with a mass of 0.140 kg and a velocity of 40.2 m/s, the de Broglie wavelength will be:###
## Step 4:For an electron with a mass of
and a velocity of
, the de Broglie wavelength will be:###
## Step 5:The de Broglie wavelength of the baseball is given as
. We can use this as a reference to compare the calculated wavelengths.## Step 6:The de Broglie wavelength of a particle is inversely proportional to its mass and velocity. Therefore, the larger the mass or the greater the velocity of the particle, the shorter the de Broglie wavelength.