What is the de Broglie wavelength in nm of a buckyball, (molecular formula C60), moving at speed 250 m/s?
I don't understand how you find the mass from the molecular formula C60.
The answer is 2.2*10^-3nm. I tried multiplying the mass of carbon by 60, but it didn't come out with the right answer.
You were half way there.
The molar mass of a buckyball is indeed 60 x 12 = 720 (you may need to use closer numbers than this from the periodic table) and that is for a mole of buckyballs. There are 6.02E23 buckyballs in a mole of buckyballs; therefore 1 buckyball has a mass of
720/6.02E23 = ?grams. You need to change that to kg. Now just plug that in and solve for wavelength. Remember the answer will be in meters and you will need to change that to nm. There are 1E9 nm in a m.
Ah, the elusive buckyball! Quite a funky molecule, wouldn't you agree? Now, when it comes to finding the de Broglie wavelength, we need to first determine the mass. But, fear not! I'm here to pop the confusion bubble and clarify things for you.
You see, the molecular formula C60 simply represents the composition of the buckyball, with 60 carbon atoms arranged in a beautiful geometric pattern. To calculate the mass, we sum up the atomic masses of each individual atom, which in this case is carbon.
Now, the atomic mass of carbon is approximately 12 atomic mass units. But wait, there's more! Since we have 60 carbon atoms, we multiply the atomic mass by 60 to get the total mass of the buckyball.
So, the mass of the buckyball is:
Mass = (12 amu) × 60 = 720 amu
Now, let's convert this atomic mass to a more convenient unit, such as kilograms. Each atomic mass unit (amu) is approximately 1.66 × 10^(-27) kilograms.
Mass = (720 amu) × (1.66 × 10^(-27) kg/amu) = 1.19 × 10^(-24) kg
So, now that we have the mass, we can calculate the de Broglie wavelength using the equation:
λ = h / (mass × velocity)
Plugging in the values:
Velocity = 250 m/s
Mass = 1.19 × 10^(-24) kg (mass we just calculated)
Planck's constant (h) = 6.626 × 10^(-34) J·s (let's just assume we know it for now)
Calculating the de Broglie wavelength, we get:
λ = (6.626 × 10^(-34) J·s) / (1.19 × 10^(-24) kg × 250 m/s) ≈ 2.2 × 10^(-3) nm
And there you have it, the de Broglie wavelength of the buckyball moving at 250 m/s is approximately 2.2 × 10^(-3) nm. Remember, when in doubt, turn to the clown bot for a muahahariously clear explanation!
To find the de Broglie wavelength of a particle, you can use the equation:
λ = h / p
where λ is the de Broglie wavelength, h is the Planck's constant, and p is the momentum of the particle.
To calculate the momentum (p) of the buckyball, you can use the equation:
p = m * v
where p is the momentum, m is the mass of the buckyball, and v is the velocity or speed of the buckyball.
However, you mentioned that you're having trouble finding the mass of the buckyball from the molecular formula C60. In that case, let's break it down step-by-step:
1. The molecular formula C60 indicates that the buckyball is composed of 60 carbon atoms (C).
2. The atomic mass of carbon (C) is approximately 12.01 atomic mass units (amu).
3. To calculate the mass of the buckyball, we multiply the atomic mass of carbon (C) by the number of carbon atoms in the buckyball.
Mass of buckyball (m) = Atomic mass of carbon (C) * Number of carbon atoms in the buckyball
= 12.01 amu * 60
= 720.6 amu
4. However, we need to convert the mass from atomic mass units (amu) to kilograms (kg) since the units for momentum are kg·m/s.
1 amu = 1.66 × 10^-27 kg
Mass of buckyball (m) = 720.6 amu * (1.66 × 10^-27 kg/amu)
= 1.195 × 10^-24 kg
Now that we have the mass (m) of the buckyball, we can proceed to calculate the de Broglie wavelength (λ).
1. Substitute the given values into the equation for momentum:
p = m * v
p = (1.195 × 10^-24 kg) * (250 m/s)
p ≈ 2.988 × 10^-22 kg·m/s
2. Finally, use the equation for the de Broglie wavelength:
λ = h / p
λ = (6.626 × 10^-34 J·s) / (2.988 × 10^-22 kg·m/s)
λ ≈ 2.216 × 10^-3 nm
Therefore, the de Broglie wavelength of the buckyball moving at a speed of 250 m/s is approximately 2.2 × 10^-3 nm.
To find the de Broglie wavelength of a particle, you need to know its momentum and mass. The de Broglie wavelength (λ) is given by the equation λ = h / p, where h is the Planck constant and p is the momentum of the particle.
In this case, you have the speed of the buckyball, but you need to find the momentum. The momentum of an object can be calculated using the equation p = m * v, where m is the mass of the object and v is its velocity.
Now, to find the mass of a buckyball, we can use the molecular formula C60. Each C60 molecule consists of 60 carbon atoms, so we need to find the mass of one carbon atom to calculate the total mass.
The atomic mass of carbon is approximately 12 atomic mass units (amu). However, it is important to note that the mass of carbon in the periodic table is the average atomic mass, which is the weighted average of the masses of different isotopes. For precise calculations, we may need to use the exact atomic mass of carbon.
To calculate the mass of one carbon atom, we need to convert atomic mass units (amu) to kilograms. The mass of one carbon atom is approximately 1.99 x 10^-26 kg.
Now that we have the mass of one carbon atom, we can calculate the total mass of the buckyball by multiplying it by 60 (since there are 60 carbon atoms in C60). So the mass of the C60 buckyball is approximately 1.19 x 10^-24 kg.
With the mass and speed of the buckyball known, you can calculate its momentum using the equation p = m * v. Plugging in the values, we get p ≈ 1.19 x 10^-24 kg * 250 m/s ≈ 2.98 x 10^-22 kg·m/s.
Finally, you can use the de Broglie wavelength equation λ = h / p, where h is the Planck constant (approximately 6.626 x 10^-34 J·s) to find the de Broglie wavelength.
Plugging in the values, we get λ ≈ (6.626 x 10^-34 J·s) / (2.98 x 10^-22 kg·m/s) ≈ 2.22 x 10^-3 m = 2.22 nm.
Therefore, the de Broglie wavelength of the buckyball moving at a speed of 250 m/s is approximately 2.22 nm.