Answer: Number of atoms: 1.82 x 10^21
Step-by-step explanation:
To calculate the number of atoms present in the sample of gold, we can use the equation:
E = Nhf
Where:
E is the total energy emitted by the sample,
N is the number of atoms,
h is the Planck's constant (approximately 6.626 x 10^-34 J·s),
f is the frequency of each photon.
We are given the total energy emitted by the sample as 12.2 kJ, which we need to convert to joules:
12.2 kJ = 12.2 x 10^3 J
The frequency of each photon is related to the threshold frequency by the equation:
f = threshold frequency
Substituting the given values:
f = 1.20 x 10^15 Hz
Now we can rearrange the equation E = Nhf to solve for N:
N = E / (hf)
Substituting the values:
N = (12.2 x 10^3 J) / ((6.626 x 10^-34 J·s) * (1.20 x 10^15 Hz))
Performing the calculation:
N ≈ 1.82 x 10^21
Therefore, the number of atoms present in the sample is approximately 1.82 x 10^21.