A certain rifle bullet has a mass of 6.45 g. Calculate the de Broglie wavelength of the bullet traveling at 1817 miles per hour.
Convert mi/hr to m/s. 1 mi/hr = 0.447 m/s.
Then wavelength = h/mv
a certain riffle bullet has a mass of 6.45 g. calculate the de broglie wavelength of the bullet traveling at 1817 miles per hour.
To calculate the de Broglie wavelength of the bullet, we can use the following formula:
λ = h / p
where λ is the de Broglie wavelength, h is the Planck's constant, and p is the momentum.
First, let's convert the mass of the bullet from grams to kilograms:
m = 6.45 g = 6.45 × 10^-3 kg
Next, let's calculate the velocity of the bullet in meters per second (m/s). We need to convert miles per hour (mph) to meters per second (m/s).
1 mile = 1609.34 meters
1 hour = 3600 seconds
v = (1817 mph) × (1609.34 m / 1 mile) / (3600 s / 1 hour)
v ≈ 814.81333 m/s (rounded to five decimal places)
Now, let's calculate the momentum of the bullet using the formula:
p = m × v
p = (6.45 × 10^-3 kg) × 814.81333 m/s
Next, let's find the value of Planck's constant, h. The value of Planck's constant is approximately 6.626 × 10^-34 Joule-seconds.
Now we can substitute the values of p and h into the formula to find the de Broglie wavelength:
λ = (6.626 × 10^-34 J·s) / (m × v)
Substituting the values:
λ = (6.626 × 10^-34 J·s) / ((6.45 × 10^-3 kg) × 814.81333 m/s)
Calculating the value using a calculator, we find:
λ ≈ 1.622 × 10^-34 meters
Therefore, the de Broglie wavelength of the bullet traveling at 1817 miles per hour is approximately 1.622 × 10^-34 meters.
To calculate the de Broglie wavelength of an object, we need to use the formula:
λ = h / p
Where λ is the de Broglie wavelength, h is the Planck's constant (h = 6.626 x 10^-34 J.s), and p is the momentum of the object.
First, we need to calculate the momentum of the bullet.
Momentum (p) can be calculated using the formula:
p = m * v
Where p is the momentum, m is the mass of the object, and v is the velocity of the object.
Given information:
Mass of the bullet (m) = 6.45 g = 0.00645 kg
Velocity of the bullet (v) = 1817 miles per hour
To calculate the velocity in meters per second, we need to convert from miles per hour to meters per second:
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, the velocity in m/s would be:
v = (1817 miles/hour) * (1609.34 meters/mile) * (1 hour/3600 seconds)
Now we can substitute the values into the momentum equation:
p = (0.00645 kg) * (1817 miles/hour) * (1609.34 meters/mile) * (1 hour/3600 seconds)
Once we have calculated the momentum, we can substitute it into the de Broglie wavelength equation:
λ = (6.626 x 10^-34 J.s) / p
Substituting the calculated momentum into the equation will give us the de Broglie wavelength of the bullet.