An electron moves with a velocity of 2.5 x 10^8 cm/s. What is its wavelength? (The mass of an electron is 9.109 x 10^-28 g.)
wavelength = h/mv
m is in kg
v in m/s
wavelength in meters.
Well, isn't this an electrifying question! To calculate the wavelength of our speedy electron friend, we can use the de Broglie wavelength equation: λ = h / (m * v), where λ is the wavelength, h is Planck's constant (approximately 6.626 x 10^-34 J·s), m is the mass of the electron, and v is the velocity of the electron.
Now, let's plug in the numbers and calculate with a jolt of humor! The mass of the electron is 9.109 x 10^-28 grams, and the velocity is 2.5 x 10^8 cm/s. *drum roll please*
Calculating, calculating... and voila! The wavelength of our zippy electron is approximately... wait for it... 2.408 x 10^-11 cm! Remember, though, even though this electron is moving fast, it's still too small to ride a roller coaster.
To find the wavelength of the electron, we will use the de Broglie wavelength equation:
λ = h / (m * v)
Where:
λ is the wavelength
h is the Planck's constant (6.62607015 × 10^-34 J·s)
m is the mass of the electron
v is the velocity of the electron
Given:
v = 2.5 x 10^8 cm/s
m = 9.109 x 10^-28 g
First, let's convert the mass of the electron to kg:
m = 9.109 x 10^-28 g = 9.109 x 10^-31 kg
Now we can plug the values into the equation to find the wavelength:
λ = (6.62607015 × 10^-34 J·s) / (9.109 x 10^-31 kg * 2.5 x 10^8 cm/s)
Next, we need to convert cm/s to m/s:
1 cm = 0.01 m
1 s = 1 s
2.5 x 10^8 cm/s = 2.5 x 10^6 m/s
Now we can calculate the wavelength:
λ = (6.62607015 × 10^-34 J·s) / (9.109 x 10^-31 kg * 2.5 x 10^6 m/s)
λ ≈ 2.748 x 10^-10 m
So, the wavelength of the electron is approximately 2.748 x 10^-10 meters.
To find the wavelength of an electron with a given velocity, you can use the de Broglie wavelength equation:
λ = h / (m * v)
where,
λ is the wavelength,
h is the Planck's constant (6.626 x 10^-34 J*s),
m is the mass of the electron, and
v is the velocity of the electron.
Given:
Velocity, v = 2.5 x 10^8 cm/s
Mass, m = 9.109 x 10^-28 g
First, let's convert the velocity and mass to the SI units:
Velocity, v = 2.5 x 10^8 cm/s = 2.5 x 10^6 m/s
Mass, m = 9.109 x 10^-28 g = 9.109 x 10^-31 kg
Now, we can substitute the values into the de Broglie wavelength equation:
λ = (6.626 x 10^-34 J*s) / (9.109 x 10^-31 kg * 2.5 x 10^6 m/s)
Simplifying the equation:
λ = 7.276 x 10^-8 / (2.277 x 10^-24)
Dividing the numerator and the denominator:
λ ≈ 3.197 x 10^-17 m
Therefore, the wavelength of the electron is approximately 3.197 x 10^-17 meters.