Question

for which state H atom wave function is non zero at nucleus.W hat are its integtation ?

Answer 1

For state n = 1  (1s orbital,  n=1, l=0, m_l = 0)   the Hydrogen atom wave function is non-zero at the nucleus.

Also for n =2,  2s orbital only ie., n=2, l=0, m_l = 0, also the wave function is non-zero at the nucleus.  For other states & orbitals, the wave function is 0 at the nucleus.

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Integration limits are from r = 0 to infinity