The Franck–Hertz experiment — quantised energy levels
An extension of the topic of energy levels and the atomic model. In a tube filled with mercury vapour the electron current rises with voltage, but drops sharply at specific, evenly spaced values — the electrons hand the atoms exactly quantised portions of energy. Proof that the atom's energy levels are quantised (Franck and Hertz, Nobel Prize 1925).
I will give you a voltage U — guess how many times the electron collides inelastically (how many excitations) before it reaches the anode. Threshold E_exc = 4.9 V.
What just happened?
Electrons accelerated by the voltage U strike mercury atoms. As long as their energy is below 4.9 eV, the collisions are elastic — the current rises with U. Once their energy reaches 4.9 eV, the electron collides inelastically: it hands the atom exactly that portion and almost stops itself — the anode current drops sharply.
The quantised portion of energy:
— the atom accepts energy only in a precisely defined "packet". e — the electron charge, ΔU — the voltage spacing between dips, ΔE — the atom's excitation energy.
Why are the dips evenly spaced?
At higher U the electron has time to excite an atom once more — hence the second, third and fourth "packet" of losses. The spacing between dips is constant, because it is still the same portion of energy:
What did this prove?
If the atom's energy were continuous, the current would rise smoothly. The evenly spaced, repeating dips prove that the atom has quantised energy levels — a direct confirmation of the Bohr model.
Why this matters for the exam:
It is the flagship proof of energy quantisation in the atom. Trick: equal spacing of the dips = one quantised portion ΔE = e·ΔU. From the voltage spacing you can calculate the atom's excitation energy.
Remember: evenly spaced current dips in the Franck–Hertz tube are the signature of the atom's quantised levels — energy is accepted only in portions ΔE = e·ΔU.
Theory & formulas
Quantised levels
In a tube filled with mercury vapour the electron current rises with voltage, but drops sharply at evenly spaced values (every ~4.9 V for mercury).
Why
Electrons lose energy in inelastic collisions, handing the atoms exactly a quantised portion — the excitation energy: Equal spacing of the dips = a fixed portion of energy. Proof of the quantisation of the atom's energy levels (Nobel Prize 1925).
Notation: — the elementary charge, — the accelerating voltage, — the atom's excitation energy.
Frequently asked questions
›What did the Franck–Hertz experiment prove?
That the atom's energy is quantised — the atom accepts energy only in specific portions.
›Why does the current drop at specific voltages?
Because the electrons reach the atom's excitation energy and lose it in inelastic collisions.
›What do the evenly spaced dips mean?
That the portion of energy (the quantum) is fixed — successive dips roughly every 4.9 V for mercury.
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