Babuta shot a total of 208.4.
A 9.5 in response to Croatia’s Miran Maricic’s 10.7 put paid to his hopes of finishing on the podium.
The 25-year-old Babuta started the final with a 10.7 and followed that with a 10.2.
A third shot of 10.5 saw him take the fourth spot while a 10.4 in his fourth attempt lifted him to the third spot. He finished the first series with a solid 10.6.
He started the second series with a 10.7, followed that with a 10.5 and shot a near-perfect 10.8 in the second shot of the first elimination series.
That effort propelled him into the second place while reducing the deficit between him and world record holder Chinese Sheng Lihao to 0.1 point.
However, he could not sustain the form and missed out on the medal.
Lihao claimed the top honours in this event with an Olympic record of 252.2. Sweden’s Victor Lindgren took the silver medal with a score of 251.4, followed by Croatia’s Miran Maricic (230) at the third spot.
Indian shooter Ramita Jindal ended seventh in the final of the 10m air rifle women’s competition.
Ramita, 20, shot 145.3 in a high-quality eight-women final.
The young Indian shooter was placed seventh after 10 shots (104.0), when the elimination began.
In danger of being eliminated, a 10.5 pushed Ramita to sixth place even as Norway’s Hegg Jeanette Duestad made an exit. But the Indian could not save herself after that.
In the qualifications on Sunday, she performed exceedingly well to make the final in the fifth place.
Ramita, the Hangzhou Asian Games bronze-medallist in the event, beat World Championship medallist Mehuli Ghosh and Tilottama Sen at the domestic trials to make it to Paris Games.
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