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A function n(x) satisfies the differential equation d² n(x)/dx² - n(x)/L² = 0 where L is a constant. The boundary conditions are: n(0)=K and n(∞)=0. The solution to this equation is

1. n(x) = K exp(x/L)
2. n(x) = K exp(-x/√L)
3. n(x) = K² exp(-x/L)
4. n(x) = K exp(-x/L)

Correct answer: n(x) = K exp(-x/L)

Solution

The correct option is right because it satisfies both the differential equation and the boundary conditions; specifically, the exponential decay form ensures that as x approaches infinity, n(x) approaches zero, while at x=0, it equals K.

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