To my Knowledge Browning or for that matter any gunmaker has never made a 16 gauge shotgun with a 4in.chamber.In order to get the answer that you seek,you will need to include the model of Browning shotgun in question along with the serial number(to date the year of manufacture) and the overall condition of your shotgun.
Tell us a little more. Sears sold a lot of different shotguns and a serial number will not identify it.
1940
IT IS WORTH ABOUT $280.OO
Rossi S A 20 gauge 3 modified, number 9101, serial number S20 SP050548 is valued at $150 in good condition. It has a 3 inch chamber and a 28 inch barrel.
Up to 200
The Springfield 20 gauge model 94-B is valued at between $75 and $100. It has a 32 inch barrel, and a 2 3/4 inch chamber.
100-325 USD
Winchester firearms
none of above mine is a 10 gauge with 3 1/2 inch chamber and in camo drilled and tapped for a scope
i just bought one for$85 in fair condition
20 gauge? Unless if your wanting to know exactly what the deminsions are like in thousandths of an inch.
Requires professional appraisal.