My mother inherited Rs.644000.Should the zakat be paid immediately or after one year. What percentage should be paids. Is it 5% or 2.5%.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If the wealth she inherited from her father reaches Nisab (i.e. equals the value of 85 grams of gold), or it reaches Nisaab after being added to her own money, she has to pay its Zakah 2.5% if the total amount has been in her possession for one complete lunar year.
Furthermore, it is her duty to pay Zakah every lunar year as long as the money equals 85 grams and has been possessed for the whole year.
Allah knows best.