To determine which equation was used by Albert Einstein to explain the photoelectric effect, let's consider the options provided and their components. In the photoelectric effect, Albert Einstein described how light can be thought of as quanta of energy called photons.
1. [tex]\( E = \frac{h}{v} \)[/tex]
- This equation suggests that energy [tex]\( E \)[/tex] is the quotient of Planck's constant [tex]\( h \)[/tex] and the frequency [tex]\( v \)[/tex]. This is not correct because frequency and Planck's constant are not related in such a way for the photoelectric effect.
2. [tex]\( E = hv \)[/tex]
- This equation implies that the energy [tex]\( E \)[/tex] of a photon is the product of Planck's constant [tex]\( h \)[/tex] and its frequency [tex]\( v \)[/tex]. This is the correct equation that Einstein used to describe the photoelectric effect. It relates the energy of a photon directly to its frequency.
3. [tex]\( E = \frac{\nu}{h} \)[/tex]
- This equation incorrectly suggests that energy [tex]\( E \)[/tex] is the frequency [tex]\( v \)[/tex] divided by Planck's constant [tex]\( h \)[/tex]. This formulation is not correct for the photoelectric effect.
4. [tex]\( E = h - v \)[/tex]
- This equation suggests a subtraction relationship between Planck’s constant [tex]\( h \)[/tex] and frequency [tex]\( v \)[/tex], which does not make sense in the context of the photoelectric effect.
Therefore, the equation used by Albert Einstein to explain the photoelectric effect is:
[tex]\[ E = hv \][/tex]
Thus, the correct answer is the second option:
[tex]\[ \boxed{2} \][/tex]
