Shortest Balmer wavelength of hydrogen equals shortest Brackett wavelength of a hydrogen-like atom: find Z

The same question, asked 2 times: 10 May 2024 S1, 19 Apr 2026 S1. Every wording below, oldest first.

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Question 1
10 May 2024 S1
47 $Shortest wavelength in Balmer series of H = shortest wavelength in Brackett series of hydrogen-like atom of atomic number z. Value of z is$
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Question 2
19 Apr 2026 S1
146 $The shortest wavelength in the Balmer series of hydrogen atom is equal to the shortest wavelength in the Brackett series of a hydrogen like atom of atomic number 'Z'. The value of 'Z' is$
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Question 1