Suppose an atom is like hydrogen but it has two protons in the nucleus and, like...

Suppose an atom is like hydrogen but it has two protons in the nucleus and, like hydrogen, has only one electron (see section 7.8). Suppose also that this atom is in the (n, l, m_l) = (3, 2, 0) state. Calculate the probability of finding the electron within a distance of 0.0529 nm.

Expert Solution

The radial part of the n = 3 wave function of the electron in the atom with Z protons is

where a = 0.0429 nm is the Bohr radius

The probaility of finding the electron between r = 0 and r = a is

Plugging in Z = 2 one obtains

The integration gives

Hence

The probability is

genius_generous answered 2 years ago

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