Final answer:
The distance between the electron and the nucleus in the first Bohr orbit, given the de Broglie wavelength of the electron, is λ. Therefore, the correct option is D.
Step-by-step explanation:
The distance between the electron and the nucleus in the first Bohr orbit can be calculated using the formula r = n^2 * (h^2 / (4π^2 * m * e^2)), where n is the principal quantum number, h is the Planck's constant, m is the mass of the electron, and e is the charge of the electron. In this case, the electron is in the first Bohr orbit, so n = 1. Therefore, the distance between the electron and the nucleus is given by r = (1)^2 * (h^2 / (4π^2 * m * e^2)). Since the de Broglie wavelength is given by λ = h / p, where p is the momentum of the electron, we can substitute λ into the equation to find the distance between the electron and the nucleus: r = λ^2 / (4π^2 * m * e^2). This means that the correct answer is d. λ.