I need help with these two problems:
1.The H-Cl bond has a frequency of vibration of 8.662 multiplied by 10^13 Hz. What wavelength (in µm) corresponds to that frequency?
-is the answer just (3.00x10^8 m*s)/(8.662x10^13 s^-1)
2.A flame has a characteristic color due to emissions of photons of wavelength 525 nm. What is the mass equivalence of 2 mol photons of this wavelength (1 J = 1 kg·m2/s2)?
For 1 you have it correct except that the problem asks for the answer in micrometers and your answer has the unit of meters.
For 2,
E = hc/wavelength.
Remember to convert wavelength from nm to meters and that will give you the energy for one photon. Multiply that by 2 to give you two photons and set that equal to mc^2 to calculate mass.
1. To find the wavelength corresponding to a frequency, you can use the equation:
Speed of light (c) = Frequency (ν) x Wavelength (λ)
Rearranging this equation to solve for wavelength, we get:
Wavelength (λ) = Speed of light (c) / Frequency (ν)
Plugging in the values given, you can use the following steps to calculate the wavelength:
Wavelength (λ) = (3.00 x 10^8 m/s) / (8.662 x 10^13 Hz)
Simplifying this expression will give you the wavelength in meters. To convert it to micrometers (µm), you need to multiply it by a conversion factor of 1 µm = 10^-6 m. So, the final calculation would be:
Wavelength (λ) in µm = (Wavelength (λ) in meters) x (10^6 µm/1 m)
2. To find the mass equivalence of photons, you can use Einstein's equation:
Energy (E) = Mass (m) x Speed of light (c)^2
Rearranging this equation to solve for mass, we get:
Mass (m) = Energy (E) / Speed of light (c)^2
First, you need to find the energy of 2 mol of photons using the wavelength given. To calculate the energy, you can use the following expression:
Energy (E) = Planck's constant (h) x Speed of light (c) / Wavelength (λ)
Given that 1 J = 1 kg·m^2/s^2 and 1 mol of photons contains Avogadro's number (6.022 x 10^23) of photons, you can calculate the mass equivalence of 2 mol of photons:
Mass (m) = (Energy (E) x 2 mol) / Speed of light (c)^2
Substituting the values and simplifying the expression should give you the mass equivalence in kg.