Hello, I have no idea how to do the following question. Any help would be appreciated:
An energy of at least 13.6 electron-volts is required to ionise a hydrogen atom. What is the longest wavelength of electromagnetic wave capable of ionising hydrogen? And which regions of the E-M spectrum correspond to photons capable of ionising hydrogen?
1) E=planck'sconstant*speedlight/wavelength
solve for wavelength.
2) http://www.astro.virginia.edu/class/oconnell/astr121/im/em-op-spectrum.gif
To determine the longest wavelength of an electromagnetic wave capable of ionizing a hydrogen atom, we can use the equation:
λ = c / ν
where λ represents the wavelength, c represents the speed of light (approximately 3 × 10^8 meters per second), and ν represents the frequency of the wave.
First, we need to find the energy associated with a photon that can ionize hydrogen. The energy required to ionize a hydrogen atom is given as 13.6 electron volts (eV). Since 1 eV is equivalent to 1.6 × 10^-19 Joules (J), we can convert the energy to Joules:
E = 13.6 eV × 1.6 × 10^-19 J/eV
Next, we can use the relationship between energy and frequency for a photon:
E = h × ν
where E is the energy, h is Planck's constant (approximately 6.63 × 10^-34 J·s), and ν is the frequency.
Rearranging the equation to solve for frequency, we get:
ν = E / h
Now we can substitute the value of E into the equation:
ν = (13.6 eV × 1.6 × 10^-19 J/eV) / (6.63 × 10^-34 J·s)
After the calculation, we obtain the value of frequency.
Finally, we can use the wavelength equation mentioned earlier to find the longest wavelength:
λ = c / ν
Substituting the value of ν into the equation, we can calculate the longest wavelength of the electromagnetic wave capable of ionizing hydrogen.
To determine which regions of the electromagnetic (E-M) spectrum correspond to photons capable of ionizing hydrogen, we need to examine the relationship between wavelength and the E-M spectrum. The E-M spectrum includes various regions such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
Generally, the E-M waves with shorter wavelengths (higher frequencies) have higher energies. Therefore, photons capable of ionizing hydrogen would be found in regions of the E-M spectrum with shorter wavelengths, such as ultraviolet, X-rays, and gamma rays.
Keep in mind that this explanation assumes the hydrogen atom is in its ground state and does not consider any additional factors that may affect ionization.