Actually I'm using 820 Ohm resistor for the LED and changed voltage to 3V. I'm starting to think that problem is in the breadboard.And you're feeding 2V into it?
A red LED generally has a voltage drop of 1.8V. Using a 2V supply and a 300 ohm resistor, that means that the current flowing through the LED is (2V-1.8V)/300 = 0.6mA. Something seems wrong there. If the LED is only seeing 0.6mA it would not be shining very brightly. So what dannyf said (besides "rectified static", which is total rubbish) is correct--it should only be lighting very faintly, even when the transistor is in saturation.
Voltage after the LED is 1V so Mr. Ohm isn't lying.
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