His son, Farouk Ibrahim Umar, confirmed the death to newsmen on Monday.
He said that the burial rites of the late renowned physicist would be held at Kofar Kudu by 10am on Tuesday (today).
The deceased, who served as BUK Vice Chancellor between 1979 and 1986, was the third head of the institution.
He was the first Nigerian academic in physics to teach at the university in 1976.
He was a member of the Nigerian delegation to the International Atomic Energy Agency General Conference from 1989 and was appointed Director-General of the Energy Commission of Nigeria in 1989.
Late Prof. Umar served as Chairman of the Board of Governors of the IAEA for 2000-2001 and in 2004, he was the Director of the Centre for Energy Research and Training, where the first Nigerian research nuclear reactor is located.
His last known appointment was in 2007, when he was on the international advisory committee for the international workshop on Renewable Energy for Sustainable Development in Africa, held at the University of Nigeria, Nsukka, Nigeria.
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