What is the Relationship Between Wavelength and Ionization Energy in Hydrogen?

In summary, the conversation discusses the calculation of energy required to ionise a Hydrogen atom by using the equation E=hc/λ. It is clarified that this equation relates to the energy and wavelength of a photon, not the deBroglie wavelength of the electron. The conversation concludes with the understanding that the equation E=hc/λ can be used to accurately calculate the energy needed to ionise the atom.
  • #1
mrausum
45
0

Homework Statement



The wavelengths λ of spectral lines produced by the Hydrogen atom are given by the expression:

7c53df3d1d6bba9ca9ba2a89f7f3baae.png
.

Calculate the Energy in eV required to ionise the atom

Homework Equations



p=h/[tex]\lambda[/tex]

The Attempt at a Solution



n2 = 1 and n1 = infinity, therefore [tex]\lambda[/tex]=1/R.

E = p2/2m = h2/([tex]\lambda[/tex]^2*2Me)

Subbing in [tex]\lambda[/tex]=1/R. and rearranging gives:

E = (h2R2)/(2Me)

Why doesn't this give me the right answer?
 
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  • #2
mrausum said:

Homework Equations



p=h/[tex]\lambda[/tex]

In that equation, λ is the deBroglie wavelength of the electron, and not the wavelength of the photon. So I'm afraid it isn't relevant here.

Instead, what other equation do you have that relates the energy and wavelength of a photon?
 
  • #3
Redbelly98 said:
In that equation, λ is the deBroglie wavelength of the electron, and not the wavelength of the photon. So I'm afraid it isn't relevant here.

Instead, what other equation do you have that relates the energy and wavelength of a photon?

So it's just as simple as using E = hc/lamda = hcR?
 
  • #5
ah i see what's going on now - the equation gives the wavelength of the emitted photon not the wavelength of the electron? Thanks.
 
  • #6
mrausum said:
ah i see what's going on now - the equation gives the wavelength of the emitted photon not the wavelength of the electron?
Yup!

Thanks.
You're welcome.
 

1. What is ionisation energy?

Ionisation energy is the amount of energy required to remove an electron from an atom or molecule. It is typically measured in units of kilojoules per mole (kJ/mol) or electron volts (eV).

2. Why is ionisation energy important for hydrogen?

Hydrogen is the simplest element with only one electron in its outermost shell. Therefore, its ionisation energy is a key factor in determining its chemical and physical properties, such as reactivity and bonding behavior.

3. How is the ionisation energy of hydrogen calculated?

The ionisation energy of hydrogen can be calculated using the Rydberg formula: En = -13.6/n2, where En is the ionisation energy in eV and n is the energy level of the electron. Alternatively, it can also be determined experimentally using spectroscopic techniques.

4. What factors affect the ionisation energy of hydrogen?

The ionisation energy of hydrogen is affected by the nuclear charge, the distance between the nucleus and the electron, and the shielding effect of inner electrons. It also increases as the energy level of the electron increases.

5. How does the ionisation energy of hydrogen compare to other elements?

The ionisation energy of hydrogen is relatively low compared to other elements due to its small atomic size and low nuclear charge. It is also lower than other elements in the same period of the periodic table, but increases as you move across a period and decrease as you move down a group.

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